Paper Info
Title
Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs
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 wellknown theorem by Chvatal and Erdos [A note on Hamilton circuits, Discrete Math. 2 (1972), pp. 111-135] states that if G satisfies alpha(G) <= kappa G), then G is hamiltonian. Flandrin and Li in 1989 showed that every 3-connected claw-free graph G with alpha(G) <= 2 kappa(G) is hamiltonian. Our characterization is also applied to show that every 2-connected claw-free graph G with alpha(G) <= 3 is hamiltonian, with only one well-characterized exceptional class.
Year
DOI
Venue
2014
10.1080/00207160.2013.858808
International Journal of Computer Mathematics
Keywords
Field
DocType
collapsible graphs,contraction characterizations,reductions,supereulerian graphs
Discrete mathematics,Indifference graph,Combinatorics,Forbidden graph characterization,Chordal graph,Cograph,Pathwidth,1-planar graph,Mathematics,Pancyclic graph,Split graph
Journal
Volume
Issue
ISSN
91
8
0020-7160
Citations 
PageRank 
References 
1
0.38
11
Authors
5
Name
Order
Citations
PageRank
Jinquan Xu1186.20
Ping Li2217.14
Zhengke Miao310.38
Keke Wang421.43
Hong-Jian Lai563197.39