Some properties of (a, b, k)-critical graphs

Abstract

Let a, b and k be nonnegative integers with 1 ? a ? b, and let G be a graph with vertex set V(G) and edge set E(G). Then a spanning subgraph F of G is called an [a, b]-factor if a ? dF (v) ? b for any v ? V(G). A graph G is said to be (a, b, k)-critical if G-D contains an [a, b]-factor for each subset D of k elements of V(G). We use |E(G)| and ?(G) to denote the size and spectral radius, respectively. In this paper, we establish a lower bound on the size and spectral radius of a graph G to ensure that G is (a, b, k)-critical, respectively.

Topics & Concepts