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A Note on the 3-Edge-Connected Supereulerian Graphs

A Note on the 3-Edge-Connected Supereulerian Graphs
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摘要 For two integers l :〉 0 and k ≥ 0, define C(l, k) to be the family of 2-edge connected graphs such that a graph G ∈ C(l, k) if and only if for every bond S lohtain in E(G) with |S| ≤3, each component of G - S has order at least (|V(G)| - k)/l. In this note we prove that if a 3- edge-connected simple graph G is in C(10, 3), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends an earlier result in [Supereulerian graphs and Petersen graph. JCMCC 1991, 9: 79-89] by Chen. For two integers l :〉 0 and k ≥ 0, define C(l, k) to be the family of 2-edge connected graphs such that a graph G ∈ C(l, k) if and only if for every bond S lohtain in E(G) with |S| ≤3, each component of G - S has order at least (|V(G)| - k)/l. In this note we prove that if a 3- edge-connected simple graph G is in C(10, 3), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends an earlier result in [Supereulerian graphs and Petersen graph. JCMCC 1991, 9: 79-89] by Chen.
出处 《Journal of Mathematical Research and Exposition》 CSCD 2010年第5期944-946,共3页 数学研究与评论(英文版)
基金 Supported by the Science Foundation of Chongqing Education Committee (Grant NoKJ100725)
关键词 supereulerian collapsible REDUCTION 3-edge-connected. supereulerian collapsible reduction 3-edge-connected.
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参考文献6

  • 1[ BONDY J A, MURTY U S R. Graph Theory with Applications [M]. American Elsevier Publishing Co., Inc., New York, 1976.
  • 2CATLIN P A. A reduction method to find spanning Eulerian suhgraphs [J]. J. Graph Theory, 1988, 12(1): 29-44.
  • 3CATLIN P A. Super-Eulerian graphs, collapsible graphs, and four-cycles [J]. Congr. Numer., 1987, 58: 233-246.
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  • 5CHEN Zhihong. Supereulerian graphs and spanning eulerian subgraphs [D]. Ph.D. Dissertation, Wayne State University, 1991.
  • 6CHEN Zhihong. Super-Eulerian graphs and the Petersen graph [J]. J. Combin. Math. Combin. Comput 1991, 9: 79-89.

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