On decompositions of a multi-graph into spanning subgraphs

Abstract

Abstract : Let G be a multi-graph, i.e., a finite graph with no loops. V(G) and E(G) denote the vertex-set and edge-set of G, respectively. For X is an element of V(G), d(x, G) denotes the degree (or valency) of x in G and m(x, G) denotes the multiplicity of edges at x in G, i.e. the minimum number m such that x is joined to any other vertex in G by at most m edges. A graph H is called a spanning subgraph of G if V(H) = V(G) and E(H) is a subset of E(G).