A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m ...
Abstract. We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items V = {1, 2, . . . , n} with sizes s1, s2 . . ....
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...
We study the two-dimensional version of the bin packing problem with conflicts. We are given a set of (two-dimensional) squares V = {1, 2, . . . , n} with sides s1, s2 . . . , sn ...
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...