Abstract. We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generaliz...
In this paper, we consider the parameterized complexity of the following problem: Given a hereditary property P on digraphs, an input digraph D and a positive integer k, does D ha...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
A cycle cover of a graph is a spanning subgraph each node of which is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k. Gi...
Following [1], we investigate the problem of covering a graph G with induced subgraphs G1, . . . , Gk of possibly smaller chromatic number, but such that for every vertex u of G, ...