Computational results on semistrong edge coloring of graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914550016638976 |
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| author | Lin, Yuquan Lin, Wensong |
| author_facet | Lin, Yuquan Lin, Wensong |
| contents | The semistrong edge coloring, as a relaxation of the well-known strong edge coloring, can be used to model efficient communication scheduling in wireless networks. An edge coloring of a graph $G$ is called \emph{semistrong} if every color class $M$ is a matching such that every edge of $M$ is incident with a vertex of degree 1 in the subgraph of $G$ induced by the endvertices of edges in $M$. The \emph{semistrong chromatic index} $χ_{ss}'(G)$ of $G$ is the minimum number of colors required for a semistrong edge coloring. In this paper, we prove that the problem of determining whether a graph $G$ has a semistrong edge coloring with $k$ colors is polynomial-time solvable for $k\le2$ and is NP-complete for $k\ge3$. For trees, we develop a polynomial-time algorithm to determine the semistrong chromatic index exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computational results on semistrong edge coloring of graphs Lin, Yuquan Lin, Wensong Combinatorics The semistrong edge coloring, as a relaxation of the well-known strong edge coloring, can be used to model efficient communication scheduling in wireless networks. An edge coloring of a graph $G$ is called \emph{semistrong} if every color class $M$ is a matching such that every edge of $M$ is incident with a vertex of degree 1 in the subgraph of $G$ induced by the endvertices of edges in $M$. The \emph{semistrong chromatic index} $χ_{ss}'(G)$ of $G$ is the minimum number of colors required for a semistrong edge coloring. In this paper, we prove that the problem of determining whether a graph $G$ has a semistrong edge coloring with $k$ colors is polynomial-time solvable for $k\le2$ and is NP-complete for $k\ge3$. For trees, we develop a polynomial-time algorithm to determine the semistrong chromatic index exactly. |
| title | Computational results on semistrong edge coloring of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.17069 |