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Volume 25, Issue 5
On $f$-Edge Cover Chromatic Index of Multigraphs

Yanbin Jia & Changqing Xu

Commun. Math. Res., 25 (2009), pp. 429-432.

Published online: 2021-07

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  • Abstract

Let $G$ be a multigraph with vertex set $V(G)$. Assume that a positive integer $f(v$) with $1 ≤ f(v) ≤ d(v)$ is associated with each vertex $v ∈ V$. An edge coloring of $G$ is called an $f$-edge cover-coloring, if each color appears at each vertex $v$ at least $f(v)$ times. Let $χ′_{fc}(G)$ be the maximum positive integer $k$ for which an $f$-edge cover-coloring with $k$ colors of $G$ exists. In this paper, we give a new lower bound of $χ′_{fc}(G)$, which is sharp.

  • Keywords

edge coloring, $f$-edge cover-coloring, $f$-edge cover.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CMR-25-429, author = {Jia , Yanbin and Xu , Changqing}, title = {On $f$-Edge Cover Chromatic Index of Multigraphs}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {5}, pages = {429--432}, abstract = {

Let $G$ be a multigraph with vertex set $V(G)$. Assume that a positive integer $f(v$) with $1 ≤ f(v) ≤ d(v)$ is associated with each vertex $v ∈ V$. An edge coloring of $G$ is called an $f$-edge cover-coloring, if each color appears at each vertex $v$ at least $f(v)$ times. Let $χ′_{fc}(G)$ be the maximum positive integer $k$ for which an $f$-edge cover-coloring with $k$ colors of $G$ exists. In this paper, we give a new lower bound of $χ′_{fc}(G)$, which is sharp.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19360.html} }
TY - JOUR T1 - On $f$-Edge Cover Chromatic Index of Multigraphs AU - Jia , Yanbin AU - Xu , Changqing JO - Communications in Mathematical Research VL - 5 SP - 429 EP - 432 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19360.html KW - edge coloring, $f$-edge cover-coloring, $f$-edge cover. AB -

Let $G$ be a multigraph with vertex set $V(G)$. Assume that a positive integer $f(v$) with $1 ≤ f(v) ≤ d(v)$ is associated with each vertex $v ∈ V$. An edge coloring of $G$ is called an $f$-edge cover-coloring, if each color appears at each vertex $v$ at least $f(v)$ times. Let $χ′_{fc}(G)$ be the maximum positive integer $k$ for which an $f$-edge cover-coloring with $k$ colors of $G$ exists. In this paper, we give a new lower bound of $χ′_{fc}(G)$, which is sharp.

Jia , Yanbin and Xu , Changqing. (2021). On $f$-Edge Cover Chromatic Index of Multigraphs. Communications in Mathematical Research . 25 (5). 429-432. doi:
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