Supereulerian Extended Digraphs |
Received:March 30, 2017 Revised:January 15, 2018 |
Key Words:
supereulerian digraph spanning closed trail eulerian digraph hamiltonian digraph arc-locally semicomplete digraph hypo-semicomplete digraph extended digraph
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Fund Project: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). |
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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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