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- W2040576723 abstract "Motivated by the Chinese Postman Problem, Boesch, Suffel, and Tindell [The spanning subgraphs of Eulerian graphs, J. Graph Theory 1 (1977), pp. 79–84] proposed the supereulerian graph problem which seeks the characterization of graphs with a spanning Eulerian subgraph. Pulleyblank [A note on graphs spanned by Eulerian graphs, J. Graph Theory 3 (1979), pp. 309–310] showed that the supereulerian problem, even within planar graphs, is NP-complete. In this paper, we settle an open problem raised by An and Xiong on characterization of supereulerian graphs with small matching numbers. A well-known theorem by Chvatal and Erdos [A note on Hamilton circuits, Discrete Math. 2 (1972), pp. 111–135] states that if G satisfies α(G)≤κ(G), then G is hamiltonian. Flandrin and Li in 1989 showed that every 3-connected claw-free graph G with α(G)≤2 κ(G) is hamiltonian. Our characterization is also applied to show that every 2-connected claw-free graph G with α(G)≤3 is hamiltonian, with only one well-characterized exceptional..." @default.
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- W2040576723 date "2014-03-26" @default.
- W2040576723 modified "2023-09-22" @default.
- W2040576723 title "Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs" @default.
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- W2040576723 doi "https://doi.org/10.1080/00207160.2013.858808" @default.
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