Existence of k-edge connected ordinary graphs with prescribed degrees

Abstract

An ordinary graph G is a set of objects called nodes and a family of unordered pairs of the nodes called edges. The degree of a node in G is the number of edges in G which contain it. G is called connected if it is not the union of two disjoint nonempty subgraphs. A graph H is called k-edge connected if deleting any fewer than k edges from H leaves a connected graph. It is proved that there exists a k-edge connected graph H for k > 1 with prescribed integer degrees di if and only if there exists an ordinary graph with these degrees and all di> k. There exists a 1-connected (i.e., connected) ordinary graph with prescribed positive integer degrees di if and only if there exists an ordinary graph with these degrees and [equation].