A SUFFICIENT CONDITION FOR A REGULAR GRAPH TO BE CLASS-1

The core G Delta of a simple graph G is the subgraph induced by the ve rtices of maximum degree. It is well known that the Petersen graph is not 1-factorizable and has property that the core of the graph obtaine d from it by removing one vertex has maximum degree 2. in this paper, we prove the following result. Let G be a regular graph of even order with d(G) greater than or equal to 3. Suppose that G contains a vertex upsilon such that the core of G\upsilon has maximum degree 2. If G is not the Petersen graph, then G is 1-factorizable. (C) 1993 John Wiley and Sons, Inc.