{"title":"Bichromatic coloring game on triangulations","authors":"Naoki Matsumoto","doi":"10.1051/ro/2023162","DOIUrl":"https://doi.org/10.1051/ro/2023162","url":null,"abstract":"In this paper, we study bichromatic coloring game on a disk triangulation, which is introduced by Aichholzer et al. in 2005. They proved that if a disk triangulation has at most two inner vertices, then the second player can force a tie in the bichromatic coloring game on the disk triangulation. We prove that the same statement holds for any disk triangulation with at most four inner vertices, and that the bound of the number of inner vertices is the best possible. Furthermore, we consider the game on topological triangulations.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135639864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reducible 3-critical graphs","authors":"Imran Allie","doi":"10.1051/ro/2023143","DOIUrl":"https://doi.org/10.1051/ro/2023143","url":null,"abstract":"In this paper, we provide further insights into the reducibility of 3-critical graphs. A graph is 3-critical if it is class two, that is, has chromatic index 4, and the removal of any one edge renders a graph with chromatic index 3. We consider two types of reductions: the suppression of a 2-connected subgraph into a single edge; and the suppression of a 3-connected subgraph into a single vertex. That is, in cases where the 2- or 3-connected subgraph is cubic or strictly subcubic. We show that every cyclically 2-connected 3-critical graph can be reduced to a smaller 3-critical graph using this method. We also prove that every 3-critical graph which is cyclically k -connected with k = 2 or k = 3, contains a 3-critical minor which is cyclically k -connected with k ≥ 4.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135248644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum weight t-sparse set problem on vector-weighted graphs","authors":"Yuquan Lin, Wensong Lin","doi":"10.1051/ro/2023145","DOIUrl":"https://doi.org/10.1051/ro/2023145","url":null,"abstract":"Let t be a nonnegative integer and G = ( V ( G ), E ( G )) be a graph. For v ∈ V ( G ), let N G ( v ) = { u ∈ V ( G ) { v } : uv ∈ E ( G )}. And for S ⊆ V ( G ), we define d S ( G ; v ) = | N G (v) ∩ S | for v ∈ S and d S ( G ; v ) = −1 for v ∈ V ( G ) S . A subset S ⊆ V ( G ) is called a t -sparse set of G if the maximum degree of the induced subgraph G [ S ] does not exceed t . In particular, a 0-sparse set is precisely an independent set. A vector-weighted graph $ (G,vec{w},t)$ is a graph G with a vector weight function $ vec{w}:V(G)to {mathbb{R}}^{t+2}$, where $ vec{w}(v)=(w(v;-1),w(v;0),dots,w(v;t))$ for each v ∈ V ( G ). The weight of a t -sparse set S in $ (G,vec{w},t)$ is defined as $ vec{w}(S,G)={sum }_v w(v;{d}_S(G;v))$. And a t -sparse set S is a maximum weight t -sparse set of $ (G,vec{w},t)$ if there is no t -sparse set of larger weight in $ (G,vec{w},t)$. In this paper, we propose the maximum weight t -sparse set problem on vector-weighted graphs, which is to find a maximum weight t -sparse set of $ (G,vec{w},t)$. We design a dynamic programming algorithm to find a maximum weight t -sparse set of an outerplane graph $ (G,vec{w},t)$ which takes O (( t + 2) 4 n ) time, where n = | V ( G )|. Moreover, we give a polynomial-time algorithm for this problem on graphs with bounded treewidth.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135297954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lennin Mallma Ramirez, Nelson Maculan, Adilson Elias Xavier, Vinicius Layter Xavier
{"title":"Dislocation hyperbolic augmented Lagrangian algorithm for nonconvex optimization ","authors":"Lennin Mallma Ramirez, Nelson Maculan, Adilson Elias Xavier, Vinicius Layter Xavier","doi":"10.1051/ro/2023153","DOIUrl":"https://doi.org/10.1051/ro/2023153","url":null,"abstract":"The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity condition. in this work, we ensure that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point, and we present computational experiments to demonstrate the performance of our proposed algorithm.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"165 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135394240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sufficient conditions for graphs to have strong parity factors","authors":"Sizhong Zhou, Yuli Zhang","doi":"10.1051/ro/2023147","DOIUrl":"https://doi.org/10.1051/ro/2023147","url":null,"abstract":"A graph G has a strong parity factor F if for every subset X ⊆ V ( G ) with | X | even, G contains a spanning subgraph F such that δ ( F ) ≥ 1, d F ( u ) ≡ 1 (mod 2) for any u ∈ X , and d F ( v ) ≡ 0 (mod 2) for any v ∈ V ( G ) X . In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"307 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135297962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Malmquist index evaluation of countries: 2000-2019","authors":"H. Farnoudkia","doi":"10.1051/ro/2023118","DOIUrl":"https://doi.org/10.1051/ro/2023118","url":null,"abstract":"One of the sophisticated mathematical techniques for evaluating the relative efficiency of decision-making units (DMUs) in a multi-inputs-outputs setting is data envelopment analysis (DEA). A non-parametric productivity index called the Malmquist index (MI) tracks changes in a DMU's overall factor output over time. This study seeks to present a broad overview of the changes in the MI for nearly all of the world's nations over 19 years beginning in 2000. This research evaluates a time series data set made up of 16 economic indexes. Each nation's MI, which compares 2000 and 2019, shows how each nation has changed over that period. One of the most important purposes of this study comparing the countries by their MI is that it allows for a fair comparison of productivity across different time periods and regions. It also provides insights into the sources of productivity growth, such as changes in technology or improvements in efficiency. As a result, the countries can allocate resources more wisely and develop more effective investment plans by understanding the elements that lead to productivity increase. By implementing some statistical techniques, nations are further divided into four categories based on their MI. Furthermore, a yearly distribution of the Malmquist Index (MI) has been included to illustrate its trends between the years 2000 to 2019. Finally, the changing flow for some countries of each category is shown in three-year tracks.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"26 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82404733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed Yusuf Waziri, Hadiza Usman Muhammad, Abubakar Sani Halilu, K. Ahmed, Salisu Murtala
{"title":"Hybrid derivative-free methods for solving system of nonlinear equations","authors":"Mohammed Yusuf Waziri, Hadiza Usman Muhammad, Abubakar Sani Halilu, K. Ahmed, Salisu Murtala","doi":"10.1051/ro/2023117","DOIUrl":"https://doi.org/10.1051/ro/2023117","url":null,"abstract":"This work presents a predictor-corrector iterative approach for solving systems of nonlinear equations. The methods are derivative-free with correction and acceleration parameters obtained via approximating the Jacobian matrix. Using an inexact line search procedure and under appropriate conditions, we proved that the proposed method is globally convergent. We, additionally, present some numerical results to show the efficiency and effectiveness of the proposed method.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"346 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78558691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The effects of green house gas costs on optimal pricing and production lotsize in an imperfect production system","authors":"Shib Sankar Sana","doi":"10.1051/ro/2023115","DOIUrl":"https://doi.org/10.1051/ro/2023115","url":null,"abstract":"The present article deals with an imperfect production system considering costs for greenhouse gas (GHG) to determine the optimal reserve selling price, sales teams' efforts and production lotsize. As per government guidelines, the manufacturer used to adopt green practices in supply chain management to meet the customers’ satisfaction regarding fair prices and quality of the products. In this connection, a mathematical model is formulated and analyzed considering various cost factors and interval values of the key parameters. Finally, numerical illustrations are considered to justify the proposed model.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"58 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79006660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Degree conditions for the existence of a {P2 ,P5}-factor in a graph","authors":"Su Wang, Wei Zhang","doi":"10.1051/ro/2023111","DOIUrl":"https://doi.org/10.1051/ro/2023111","url":null,"abstract":"A subgraph of a graph $G$ is spanning if the subgraph covers all vertices of $G$. A path-factor of a graph $G$ is a spanning subgraph $H$ of $G$ such that every component of $H$ is a path. In this article, we prove that (romannumeral1) a connected graph $G$ with $delta(G)geq5$ admits a ${P_2,P_5}$-factor if $G$ satisfies $delta(G)>frac{3alpha(G)-1}{4}$; (romannumeral2) a connected graph $G$ of order $n$ with $ngeq7$ has a ${P_2,P_5}$-factor if $G$ satisfies $max{d_G(x),d_G(y)}geqfrac{3n}{7}$ for any two nonadjacent vertices $x$ and $y$ of $G$.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"77 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85521607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The investment and reinsurance game of insurers and reinsurers with default risk under CEV model","authors":"Wenjing Hao, Zhijian Qiu, Lu Li","doi":"10.1051/ro/2023112","DOIUrl":"https://doi.org/10.1051/ro/2023112","url":null,"abstract":"On the premise of considering the interests of insurance companies and reinsurance companies at the same time, this paper studies the investment and reinsurance game between them. Suppose that the compensation process faced by an insurance company is described by Brownian motion with drift. Insurance companies can purchase proportional reinsurance from reinsurance companies, and both companies can invest in a risk-free asset, a risky asset whose price process follows the constant elasticity of variance (CEV) model, and a defaultable bond. With the goal of maximizing the expected utility of weighted terminal wealth, the corresponding Hamilton-Jacobi-Bellman (HJB) equations are established and solved by using the principle of dynamic programming, and the analytical expressions of the equilibrium investment-reinsurance strategies of insurers and reinsurers are derived respectively. Finally, the influence of each model parameter on the equilibrium strategy is analyzed by numerical examples.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"39 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77725785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}