Supereulerian Extended Digraphs
Received:March 30, 2017  Revised:January 15, 2018
Key Word: supereulerian digraph   spanning closed trail   eulerian digraph   hamiltonian digraph   arc-locally semicomplete digraph   hypo-semicomplete digraph   extended digraph
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11761071; 61363020), Science and Technology Innovation Project of Xinjiang Normal University (Grant No.XSY201602013), the "13th Five-Year'' Plan for Key Discipline Mathematics of Xinjiang Normal University (Grant No.17SDKD1107).
 Author Name Affiliation Changchang DONG College of Mathematics Sciences, Xinjiang Normal University, Xinjiang 830017, P. R. China Juan LIU College of Mathematics Sciences, Xinjiang Normal University, Xinjiang 830017, P. R. China
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Abstract:
A digraph $D$ is supereulerian if $D$ has a spanning eulerian subdigraph. Bang-Jensen and Thomass\'{e} conjectured that if the arc-strong connectivity $\lambda(D)$ of a digraph $D$ is not less than the independence number $\alpha(D)$, then $D$ is supereulerian. In this paper, we prove that if $D$ is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying $\lambda(D)\geq \alpha(D)$, then $D$ is supereulerian.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.02.001
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