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- W3154409465 abstract "A star edge coloring of a graph is a proper edge coloring with no $2$-colored path or cycle of length four. The star chromatic index $chi'_{st}(G)$ of $G$ is the minimum number $t$ for which $G$ has a star edge coloring with $t$ colors. We prove upper bounds for the star chromatic index of complete bipartite graphs; in particular we obtain tight upper bounds for the case when one part has size at most $3$. We also consider bipartite graphs $G$ where all vertices in one part have maximum degree $2$ and all vertices in the other part has maximum degree $b$. Let $k$ be an integer ($kgeq 1$), we prove that if $b=2k+1$ then $chi'_{st}(G) leq 3k+2$; and if $b=2k$, then $chi'_{st}(G) leq 3k$; both upper bounds are sharp. Finally, we consider the well-known conjecture that subcubic graphs have star chromatic index at most $6$; in particular we settle this conjecture for cubic Halin graphs." @default.
- W3154409465 created "2021-04-26" @default.
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- W3154409465 date "2021-07-01" @default.
- W3154409465 modified "2023-10-14" @default.
- W3154409465 title "On star edge colorings of bipartite and subcubic graphs" @default.
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- W3154409465 doi "https://doi.org/10.1016/j.dam.2021.03.007" @default.
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