Bohn, Adam Faenza, Yuri Fiorini, Samuel Fisikopoulos, Vissarion Macchia, Marco Pashkovich, Kanstantsin
Published in
Mathematical Programming Computation

A (convex) polytope P is said to be 2-level if for each hyperplane H that supports a facet of P, the vertices of P can be covered with H and exactly one other translate of H. The study of these polytopes is motivated by questions in combinatorial optimization and communication complexity, among others. In this paper, we present the first algorithm ...

Das, Angsuman
Published in
Discussiones Mathematicae - General Algebra and Applications

In this short paper, we characterize the positive integers n for which intersection graph of ideals of ℤn is perfect.

Chudnovsky, Maria Scott, Alex Seymour, Paul
Published in
Combinatorica

We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ.

Benchetrit, Yohann
Published in
Mathematical Programming

We prove that every h-perfect line graph and every t-perfect claw-free graph G has the integer round-up property for the chromatic number: for every non-negative integral weight function c on the vertices of G, the weighted chromatic number of (G, c) can be obtained by rounding up its fractional relaxation. As a corollary, we obtain that the weight...

Pal, Madhumangal Pal, Anita
Published in
International Journal of Applied and Computational Mathematics

In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration of two programme slots have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a progr...

Farrokhi, M.D.G. Mohammadian, A.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

Bruhn, Henning Stein, Maya
Published in
Mathematical Programming

A graph is called t-perfect, if its stable set polytope is defined by non-negativity, edge and odd-cycle inequalities. We characterise the class of all claw-free t-perfect graphs by forbidden t-minors, and show that they are 3-colourable. Moreover, we determine the chromatic number of claw-free h-perfect graphs and give a polynomial-time algorithm ...

Andres, Stephan Dominique
Published in
Mathematical Methods of Operations Research

A graph coloring game introduced by Bodlaender (Int J Found Comput Sci 2:133–147, 1991) as coloring construction game is the following. Two players, Alice and Bob, alternately color vertices of a given graph G with a color from a given color set C, so that adjacent vertices receive distinct colors. Alice has the first move. The game ends if no move...

Conforti, Michele Cornuéjols, Gérard Zambelli, Giacomo
Published in
Combinatorica

In this paper we show that, if G is a Berge graph such that neither G nor its complement \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \ifmmode\expandafter\bar\else\...

Bonomo, Flavia Durán, Guillermo Lin, Min Chih Szwarcfiter, Jayme L
Published in
Mathematical Programming

Berge defined a hypergraph to be balanced if its incidence matrix is balanced. We consider this concept applied to graphs, and call a graph to be balanced when its clique matrix is balanced. Characterizations of balanced graphs by forbidden subgraphs and by clique subgraphs are proved in this work. Using properties of domination we define four subc...