Paul A. Catlin

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A graph is supereulerian if it has a spanning eulerian subgraph. There is a reduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereulerian graphs, the(More)
Let O(G) denote the set of odd-degree vertices of a graph G. Let t E N and let 9, denote the family of graphs G whose edge set has a partition f ( G ) = E, U E2 U U 15,. such that O(G) = O(G[€,]) (1 5 i 5 t ) . This partition is associated with a double cycle cover of G. We show that if a graph G is at most 5 edges short of being 4-edge-connected, then(More)