A new condition on dominated pair degree sum for a digraph to be supereulerian
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909229522092032 |
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| author | Dong, Changchang Meng, Jixiang Liu, Juan |
| author_facet | Dong, Changchang Meng, Jixiang Liu, Juan |
| contents | A digraph $D$ is supereulerian if $D$ contains a spanning eulerian subdigraph.
For any two vertices $u,v$ in a digraph $D$, if $(u,w),(v,w)\in A(D)$ for some $w\in V(D)$, then we call the pair $\{u, v\}$ dominating; if $(w,u),(w,v)\in A(D)$ for some $w\in V(D)$, then we call the pair $\{u, v\}$ dominated. In 2015, Bang-Jensen and Maddaloni [Journal of graph theory, 79(1) (2015) 8-20]
proved that if a strong digraph $D$ with $n$ vertices satisfies
$d(u) + d(v)\geq 2n -3$ for any pair of nonadjacent vertices $\{u,v\}$ of $D$, then $D$ is supereulerian. In this paper, we study the above degree sum condition for any pair of dominated or dominating nonadjacent vertices of supereulerian digraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new condition on dominated pair degree sum for a digraph to be supereulerian Dong, Changchang Meng, Jixiang Liu, Juan Combinatorics A digraph $D$ is supereulerian if $D$ contains a spanning eulerian subdigraph. For any two vertices $u,v$ in a digraph $D$, if $(u,w),(v,w)\in A(D)$ for some $w\in V(D)$, then we call the pair $\{u, v\}$ dominating; if $(w,u),(w,v)\in A(D)$ for some $w\in V(D)$, then we call the pair $\{u, v\}$ dominated. In 2015, Bang-Jensen and Maddaloni [Journal of graph theory, 79(1) (2015) 8-20] proved that if a strong digraph $D$ with $n$ vertices satisfies $d(u) + d(v)\geq 2n -3$ for any pair of nonadjacent vertices $\{u,v\}$ of $D$, then $D$ is supereulerian. In this paper, we study the above degree sum condition for any pair of dominated or dominating nonadjacent vertices of supereulerian digraphs. |
| title | A new condition on dominated pair degree sum for a digraph to be supereulerian |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.15841 |