We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to kn...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...
Abstract. An undirected graph G = (V, E) is the k-power of an undirected tree T = (V, E ) if (u, v) ∈ E iff u and v are connected by a path of length at most k in T. The tree T ...
Given a graph G and an integer k, two players alternatively color the edges of G using k colors so that adjacent edges get different colors. The game chromatic index g(G) is the m...
Andrew Beveridge, Tom Bohman, Alan M. Frieze, Oleg...
Abstract. It it shown that the first-order theory of an automatic structure, whose Gaifman graph has bounded degree, is decidable in doubly exponential space (for injective automa...