Contemporary Trends in Discrete Mathematics最新文献_第2页

Intersection graphs of Jordan arcs 约当弧的交点图

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/02

Patrice Ossona de Mendez, H. D. Fraysseix

引用次数: 0

On the minimum number of edges giving maximum oriented chromatic number 在最小的边数上给出最大的定向色数

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/12

A. Kostochka, T. Luczak, G. Simonyi, É. Sopena

{"title":"On the minimum number of edges giving maximum oriented chromatic number","authors":"A. Kostochka, T. Luczak, G. Simonyi, É. Sopena","doi":"10.1090/dimacs/049/12","DOIUrl":"https://doi.org/10.1090/dimacs/049/12","url":null,"abstract":"We show that the minimum number of edges in a graph on n vertices with oriented chromatic number n is (1 + o(1))n log2 n. In 1995, in a conversation with the French member of the set of the authors of this note, Pal Erdős asked about the minimal number of edges a graph on n vertices with oriented chromatic number n can have. During the conference on the Future of Discrete Mathematics in the cosy but fruitful atmosphere of the Stǐŕin Castle we found an elementary answer to this question which we present below. 1 Novosibirsk State University, Novosibirsk, Russia 630090. Research partially supported by the grant 96-01-01614 of the Russian Foundation for Fundamental Research and by the Cooperative Grant Award RM1-181 of the US Civilian Research and Development Foundation. Department of Discrete Mathematics, Adam Mickiewicz University, 60-769 Poznan, Poland. Research partially supported by KBN grant 2 P03A 023 09. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B.127, Budapest H-1364, Hungary. Research partially supported by the Hungarian National Foundation for Scientific Research (OTKA) Grant Nos. F023442 and T016386. LaBRI, Universite Bordeaux I, 33405 Talence Cedex, France. Research partially supported by the Barrande Grant no. 97137. After the final version of this note had been sent to the publisher we were informed that a very similar result had been proved independently by Z. Furedi, P. Horak, C. M. Pareek and X. Zhu in the paper Minimal oriented graphs of diameter 2, which is to appear in Graphs and Combinatorics.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"24 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":"134109914","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: 16

New trends in the theory of graph colorings: Choosability and list coloring 图着色理论的新动向:可选择性和列表着色

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/13

Jan Kratochvíl, Z. Tuza, M. Voigt

引用次数: 65

Topological minors in graphs of minimum degree n 最小次数为n的图中的拓扑副式

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/14

W. Mader

引用次数: 14

How to solve a Turán type extremal graph problem? (Linear decomposition) 如何解决一个Turán型极值图问题?(线性分解)

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/21

M. Simonovits

引用次数: 18

Spectra, graphs, and proteins. Towards understanding of protein folding 光谱，图形和蛋白质。对蛋白质折叠的理解

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/18

P. Pančoška, V. Janota, J. Nesetril

引用次数: 2

The generalized matching problem on partial $k$-trees 偏k树上的广义匹配问题

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/09

Arvind Gupta, Damon Kaller, Sanjeev Mahajan, T. Shermer

引用次数: 0

Graceful matchings in finite fields, the factor-difference sets of integers, and integers of the form a2 + kb2 有限域中的优美匹配，整数的因子差分集，以及形式为a2 + kb2的整数

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/20

M. Rosenfeld

引用次数: 0

Meaningless statements 毫无意义的语句

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/19

F. Roberts

{"title":"Meaningless statements","authors":"F. Roberts","doi":"10.1090/dimacs/049/19","DOIUrl":"https://doi.org/10.1090/dimacs/049/19","url":null,"abstract":"Increasingly, discrete mathematics is influenced by connections with other fields. We give one example of a broad topic in the field of discrete mathematics that comes from the social sciences, and in particular from the theory of measurement that has been developed to put measurement, especially in the social sciences, on a firm mathematical foundation. The key concept is that of meaningful statement, a statement whose truth or falsity remains unchanged after admissible transformations of scales of measurement. We apply this concept to combinatorial optimization, graph coloring, scheduling, linear programming, 0-1 optimization, and multiperson games. 1. The Future of Discrete Mathematics Increasingly, discrete mathematics is influenced by connections with other fields. In the mathematical sciences, it is influenced by connection with probability, geometry, algebra, analysis, topology, number theory, . . . Outside the mathematical sciences, it is influenced by connection with biology, chemistry, physics, manufacturing, engineering, . . . In this paper, I will give one example of a broad topic in the field of discrete mathematics that comes from the social sciences, but has been developed not only by economists and psychologists, but also by philosophers of science, physicists, logicians, and, of course, mathematicians. It is motivated by the theory of measurement that has been developed to put measurement, especially in the social sciences, on a firm mathematical foundation. In this paper, I will give a brief overview of measurement theory and define a central concept of the theory, that of a meaningful statement. I will then apply the theory of meaningfulness to discrete mathematics in various ways. In particular, I will ask whether or not statements in combinatorial optimization, that a specific solution is optimal, are meaningful. I will talk about the meaningfulness of conclusions about the generalization of graph coloring called T -coloring. I will give a variety of examples of meaningful and meaningless conclusions about scheduling problems. This will lead to the question of when a greedy solution to an optimization problem is a meaningful optimal solution. I will talk in general about 1991 Mathematics Subject Classification. Primary 90.30; Secondary 05C, 05.55, 90C, 90.50, 90.70, 90.99, 92G. The author thanks the U.S. National Science Foundation for its support under grants SBR9709134 and INT96-05174 to Rutgers University. c ©0000 American Mathematical Society 1052-1798/00 $1.00 + $.25 per page","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"62 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":"116121894","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: 4

Finding minimum weighted generators of a path system 寻找路径系统的最小加权生成器

Contemporary Trends in Discrete Mathematics Pub Date : 1900-01-01 DOI: 10.1090/dimacs/049/07

A. Frank

引用次数: 10