The strong chromatic number, S(G), of an n-vertex graph G is the smallest number k such that after adding kn/k-n isolated vertices to G and considering any partition of the vertic...
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...
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...
A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping from V (G) to V (H), that is (x)(y) is an arc in H whenever xy is an arc in G. The orie...