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.
基金
Supported by the Science Foundation of Chongqing Education Committee (Grant NoKJ100725)
