The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
The (k, r)-center problem asks whether an input graph G has ≤ k vertices (called centers) such that every vertex of G is within distance ≤ r from some center. In this paper we ...
Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Ha...