Some results on the palette index of graphs
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3
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Given a proper edge coloring $\varphi$ of a graph $G$, we define the palette $S_{G}(v,\varphi)$ of a vertex $v \in V(G)$ as the set of all colors appearing on edges incident with $v$. The palette index $\check s(G)$ of $G$ is the minimum number of distinct palettes occurring in a proper edge coloring of $G$. In this paper we give various upper and lower bounds on the palette index of $G$ in terms of the vertex degrees of $G$, particularly for the case when $G$ is a bipartite graph with small vertex degrees. Some of our results concern $(a,b)$-biregular graphs; that is, bipartite graphs where all vertices in one part have degree $a$ and all vertices in the other part have degree $b$. We conjecture that if $G$ is $(a,b)$-biregular, then $\check{s}(G)\leq 1+\max\{a,b\}$, and we prove that this conjecture holds for several families of $(a,b)$-biregular graphs. Additionally, we characterize the graphs whose palette index equals the number of vertices.
@article{DMTCS_2019_21_3_a10,
author = {Casselgren, C. J. and Petrosyan, Petros A.},
title = {Some results on the palette index of graphs},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {21},
number = {3},
year = {2019},
doi = {10.23638/DMTCS-21-3-11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-11/}
}
TY - JOUR AU - Casselgren, C. J. AU - Petrosyan, Petros A. TI - Some results on the palette index of graphs JO - Discrete mathematics & theoretical computer science PY - 2019 VL - 21 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-11/ DO - 10.23638/DMTCS-21-3-11 LA - en ID - DMTCS_2019_21_3_a10 ER -
%0 Journal Article %A Casselgren, C. J. %A Petrosyan, Petros A. %T Some results on the palette index of graphs %J Discrete mathematics & theoretical computer science %D 2019 %V 21 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-11/ %R 10.23638/DMTCS-21-3-11 %G en %F DMTCS_2019_21_3_a10
Casselgren, C. J.; Petrosyan, Petros A. Some results on the palette index of graphs. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3. doi: 10.23638/DMTCS-21-3-11
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