{"title":"Density","authors":"J. Nesetril, Claude Tardif","doi":"10.1090/dimacs/049/17","DOIUrl":"https://doi.org/10.1090/dimacs/049/17","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123375697","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}
{"title":"On the limit values of probabilities for the first order properties of graphs","authors":"J. Spencer, L. Thoma","doi":"10.1090/dimacs/049/23","DOIUrl":"https://doi.org/10.1090/dimacs/049/23","url":null,"abstract":"Consider the random graph ${cal G}(n,p),$ where $p=p(n)$ is any threshold function satisfying $p(n) = Theta(ln n / n).$ We give a full characterization of the limit values of probabilities of ${cal G}(n,p)$ having a property $psi,$ where $psi$ is any sentence of the first order theory of graphs.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116350503","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}
{"title":"Linear and nonlinear systems: A survey","authors":"J. Díaz, M. Serna, P. Spirakis","doi":"10.1090/dimacs/049/03","DOIUrl":"https://doi.org/10.1090/dimacs/049/03","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116596519","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}
{"title":"Ramsey theory and partially ordered sets","authors":"W. T. Trotter","doi":"10.1090/dimacs/049/24","DOIUrl":"https://doi.org/10.1090/dimacs/049/24","url":null,"abstract":"Over the past 15 years, Ramsey theoretic techniques and concepts have been applied with great success to partially ordered sets. In the last year alone, four new applications of Ramsey theory to posets have produced solutions to some challenging combinatorial problems. First, Kierstead and Trotter showed that dimension for interval orders can be characterized by a single ramsey trail by proving that interval orders of sufficiently large dimension contain all small interval orders as subposets. Second, Winkler and Trotter introduced a notion of Ramsey theory for probability spaces and used the resulting theroy to show that interval orders can have fractional dimension arbitrarily close to 4. Third, Felsner, Fishburn and Trotter developed an extension of the product Ramsey theorem to show that there exists a finite 3-dimensional poset which is not a sphere order. Fourth, Agnarsson, Felsner and Trotter combined Ramsey theoretic techniques with other combinatorial tools to determine an asymtotic formula for the maximum number of edges in a graph whose incidence poset has dimension at most 4. In this paper, we outline how these applications were developed. Full details will appear in individual journal articles. This article also includes a brief sketch of how the applications of Ramsey theoretic techniques to posets have evolved.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129701154","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}
{"title":"Induced monochromatic subconfigurations","authors":"J. Nesetril, J. Solymosi, P. Valtr","doi":"10.1090/dimacs/049/16","DOIUrl":"https://doi.org/10.1090/dimacs/049/16","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133723221","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}
{"title":"On the structure of large homothetic subsets","authors":"G. Elekes","doi":"10.1090/dimacs/049/05","DOIUrl":"https://doi.org/10.1090/dimacs/049/05","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129402923","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}
{"title":"Oriented list colouring of undirected graphs","authors":"A. Sali, G. Simonyi","doi":"10.1090/dimacs/049/22","DOIUrl":"https://doi.org/10.1090/dimacs/049/22","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131291361","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}
{"title":"Bases of cocycle lattices and submatrices of a Hadamard matrix","authors":"Winfried Hochstättler, M. Loebl","doi":"10.1090/dimacs/049/10","DOIUrl":"https://doi.org/10.1090/dimacs/049/10","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129312497","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}
{"title":"Parameterized complexity: A framework for systematically confronting computational intractability","authors":"R. Downey, M. Fellows, U. Stege","doi":"10.1090/dimacs/049/04","DOIUrl":"https://doi.org/10.1090/dimacs/049/04","url":null,"abstract":"In this paper we give a programmatic overview of parame-terized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how xed-parameter tractability techniques can deliver practical algorithms in two diierent ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT ker-nelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artiicial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W1]. As a corollary, this implies that k-Step Reachability for Petri Nets is complete for W1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph k-Coloring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122374502","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}
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