Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...
Given a graph G = (V, E), a (d, k)-coloring is a function from the vertices V to colors {1, 2, . . . , k} such that any two vertices within distance d of each other are assigned di...
In our work we present a new approach to the problem of channel assignment in Wireless Ad Hoc Network. We introduce a new algorithm which works in distributed model of computations...
For a graph G and an integer t we let mcct(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having ...