We study vertex colorings of the square G2 of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G2 as a function of...
A sequence of the form s1s2 . . . sms1s2 . . . sm is called a repetition. A vertex-coloring of a graph is called nonrepetitive if none of its paths is repetitively colored. We ans...
In this paper, we study homomorphisms of 2-edge-colored graphs, that is graphs with edges colored with two colors. We consider various graph classes (outerplanar graphs, partial 2...
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...