Supereulerianity of k-edge-connected graphs with a restriction on small bonds

  • Authors:

  • Zhaohong Niu;Liming Xiong

  • Affiliations:

  • Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China and Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2010

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Abstract

Let k=1,l0,m=0 be integers, and let C"k(l,m) denote the graph family such that a graph G of order n is in C"k(l,m) if and only if G is k-edge-connected such that for every bond S@?E(G) with |S|@?3, each component of G-S has order at least (n-m)/l. In this paper, we show that if G@?C"3(10,m) with n11m, then either G is supereulerian or it is contractible to the Petersen graph. A graph is s-supereulerian if it has a spanning even subgraph with at most s components. We also prove the following: if G@?C"3(l,m) with n(l+1)m and l=10, then G is @?(l-4)/2@?-supereulerian; if G@?C"2(l,0) with 6@?l@?10, then G is (l-4)-supereulerian; if G@?C"2(l,m) with n(l+1)m and l=4, then G is (l-3)-supereulerian.