A colored mixed graph has vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (arc-color preserving) homomorphism from G to H . We study in this paper the colored mixed chromatic number of planar graphs, partial 2-trees and outerplanar graphs with given girth.

We deal with different algorithmic questions regarding properly arc-colored s-t trails, paths and circuits in arc-colored digraphs. Given an arc-colored digraph D with c ≥ 2 colors, we show that the problem of determining the maximum number of arc disjoint properly arc-colored s-t trails can be solved in polynomial time. Surprisingly, we prove that the determination of a properly arc-colored s-...

Introduction: It has been shown that low levels of pigmentation increase susceptibility to noise-induced hearing loss in humans. For this reason, white populations develop more pronounced noise- induced hearing loss in comparison to black populations. Similarly, blue-eyed individuals exhibit greater temporary threshold shift than brown-eyed subjects; still, no strong correlation has been veri...

The famous Chinese Postman Problem (CPP) is polynomial time solvable on both undirected and directed graphs. Gutin et al. [Discrete Applied Math 217 (2016)] generalized these results by proving that CPP on c-edge-colored graphs is polynomial time solvable for every c ≥ 2. In CPP on weighted edge-colored graphs G, we wish to find a minimum weight properly colored closed walk containing all edges...

Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum colored degree greater than or equal to d 2 e has properly edge-colored cycles of all possible lengths, including hamiltonian c...

introduction: it has been shown that low levels of pigmentation increase susceptibility to noise-induced hearing loss in humans. for this reason, white populations develop more pronounced noise- induced hearing loss in comparison to black populations. similarly, blue-eyed individuals exhibit greater temporary threshold shift than brown-eyed subjects; still, no strong correlation has been verifi...