We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
Beck introduced the concept of Ramsey games by studying the game versions of Ramsey and van der Waerden theorems. We contribute to this topic by investigating games corresponding ...
. Dirac. Some theorems on abstract graphs. Proc. London Math. Soc. (3), 2:69–81, 1952. [2] Hikoe Enomoto and Katsuhiro Ota. Partitions of a graph into paths with prescribed endve...
We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr, Erd˝os, and Lov´asz. We determine the corresponding graph parameter fo...