A defining set (of vertex coloring) of a graph G is a set of vertices S with an assignment of colors to its elements which has a unique completion to a proper coloring of G. We de...
Hossein Hajiabolhassan, Mojtaba L. Mehrabadi, Ruzb...
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 graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H o...
We consider the following vertex coloring problem. We are given an undirected graph G = (V, E), where each vertex v is associated with a penalty rejection cost rv. We need to choos...
—We investigate a new class of codes for the optimal covering of vertices in an undirected graph Gsuch that any vertex in G can be uniquely identified by examining the vertices ...
Mark G. Karpovsky, Krishnendu Chakrabarty, Lev B. ...