SIAM J. Discret. Math.最新文献_第4页

Hanani-Tutte and Hierarchical Partial Planarity Hanani-Tutte和层次部分平面性

SIAM J. Discret. Math. Pub Date : 2022-11-21 DOI: 10.1137/21m1464749

M. Schaefer

引用次数: 0

The Lower Bound Theorem for $d$-Polytopes with $2{d}+1$ Vertices $2{d}+1$顶点的$d$-多边形的下界定理

SIAM J. Discret. Math. Pub Date : 2022-11-21 DOI: 10.1137/21m144832x

Guillermo Pineda-Villavicencio, D. Yost

引用次数: 0

Decomposition of class II graphs into two class I graphs 将II类图分解为两个I类图

SIAM J. Discret. Math. Pub Date : 2022-11-11 DOI: 10.48550/arXiv.2211.05930

Yan Cao, Guangming Jing, Rong Luo, V. Mkrtchyan, Cun-Quan Zhang, Yue Zhao

引用次数: 0

On completely regular codes with minimum eigenvalue in geometric graphs 几何图中最小特征值的完全正则码

SIAM J. Discret. Math. Pub Date : 2022-10-20 DOI: 10.48550/arXiv.2210.11184

I. Mogilnykh, K. Vorob'ev

引用次数: 1

Simplicial Complexes Satisfying Serre's Condition versus the Ones Which Are Cohen-Macaulay in a Fixed Codimension 满足Serre条件的简单复形与固定余维的Cohen-Macaulay复形

SIAM J. Discret. Math. Pub Date : 2022-10-19 DOI: 10.1137/21m1439687

M. R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

引用次数: 1

New infinite families of near MDS codes holding $t$-designs and optimal locally recoverable codes 新的无限族的近MDS码持有$t$-设计和最优的局部可恢复码

SIAM J. Discret. Math. Pub Date : 2022-10-11 DOI: 10.48550/arXiv.2210.05194

Ziling Heng, Xinran Wang

引用次数: 3

Globally Rigid Augmentation of Rigid Graphs 刚性图的全局刚性增广

SIAM J. Discret. Math. Pub Date : 2022-10-06 DOI: 10.1137/21m1432417

C. Király, András Mihálykó

{"title":"Globally Rigid Augmentation of Rigid Graphs","authors":"C. Király, András Mihálykó","doi":"10.1137/21m1432417","DOIUrl":"https://doi.org/10.1137/21m1432417","url":null,"abstract":". We consider the following augmentation problem: Given a rigid graph G = ( V,E ), 3 ﬁnd a minimum cardinality edge set F such that the graph G (cid:48) = ( V,E ∪ F ) is globally rigid. We 4 provide a min-max theorem and a polynomial-time algorithm for this problem for several types of 5 rigidity, such as rigidity in the plane or on the cylinder. Rigidity is often characterized by some 6 sparsity properties of the underlying graph and global rigidity is characterized by redundant rigidity 7 (where the graph remains rigid after deleting an arbitrary edge) and 2-or 3-vertex-connectivity. 8 Hence, to solve the above-mentioned problem, we deﬁne and solve polynomially a combinatorial 9 optimization problem family based on these sparsity and connectivity properties. This family also 10 includes the problem of augmenting a k -tree-connected graph to a highly k -tree-connected and 2-11 connected graph. Moreover, as an interesting consequence, we give an optimal solution to the 12 so-called global rigidity pinning problem, where we aim to ﬁnd a minimum cardinality vertex set X 13 for a rigid graph G = ( V,E ), such that the graph G + K X is globally rigid in R 2 where K X denotes 14 the complete graph on the vertex set X .","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90781249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Refined List Version of Hadwiger's Conjecture 哈维格猜想的精炼列表版本

SIAM J. Discret. Math. Pub Date : 2022-09-15 DOI: 10.5817/cz.muni.eurocomb23-071

Yan Gu, Yiting Jiang, D. Wood, Xuding Zhu

{"title":"Refined List Version of Hadwiger's Conjecture","authors":"Yan Gu, Yiting Jiang, D. Wood, Xuding Zhu","doi":"10.5817/cz.muni.eurocomb23-071","DOIUrl":"https://doi.org/10.5817/cz.muni.eurocomb23-071","url":null,"abstract":"Assume $lambda={k_1,k_2, ldots, k_q}$ is a partition of $k_{lambda} = sum_{i=1}^q k_i$. A $lambda$-list assignment of $G$ is a $k_lambda$-list assignment $L$ of $G$ such that the colour set $bigcup_{v in V(G)}L(v)$ can be partitioned into $lambda= q$ sets $C_1,C_2,ldots,C_q$ such that for each $i$ and each vertex $v$ of $G$, $L(v) cap C_i ge k_i$. We say $G$ is emph{$lambda$-choosable} if $G$ is $L$-colourable for any $lambda$-list assignment $L$ of $G$. The concept of $lambda$-choosability is a refinement of choosability that puts $k$-choosability and $k$-colourability in the same framework. If $lambda$ is close to $k_lambda$, then $lambda$-choosability is close to $k_lambda$-colourability; if $lambda$ is close to $1$, then $lambda$-choosability is close to $k_lambda$-choosability. This paper studies Hadwiger‘s Conjecture in the context of $lambda$-choosability. Hadwiger‘s Conjecture is equivalent to saying that every $K_t$-minor-free graph is ${1 star (t-1)}$-choosable for any positive integer $t$. We prove that for $t ge 5$, for any partition $lambda$ of $t-1$ other than ${1 star (t-1)}$, there is a $K_t$-minor-free graph $G$ that is not $lambda$-choosable. We then construct several types of $K_t$-minor-free graphs that are not $lambda$-choosable, where $k_lambda - (t-1)$ gets larger as $k_lambda-lambda$ gets larger.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83341469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

The Natural Matroid of an Integer Polymatroid 整数多边形的自然矩阵

SIAM J. Discret. Math. Pub Date : 2022-09-08 DOI: 10.1137/22m1521122

Joseph E. Bonin, C. Chun, Tara Fife

引用次数: 2

The Excluded Minors for Three Classes of 2-Polymatroids Having Special Types of Natural Matroids 具有特殊类型天然拟阵的3类2-多拟阵的排除子类

SIAM J. Discret. Math. Pub Date : 2022-09-08 DOI: 10.1137/22m1521134

Joseph E. Bonin, Kevin Long

引用次数: 2