Geodesic
On the palette index of unicycle and bicycle graphs
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 3-12

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a proper edge coloring $\phi$ of a graph $G$, we define the palette $S_G(v,\phi)$ of a vertex $v \in V(G)$ as the set of all colors appearing on edges incident with $v$. The palette index $cyc(G)$ of $G$ is the minimum number of distinct palettes occurring in a proper edge coloring of $G$. In this paper we give an upper bound on the palette index of a graph $G$, in terms of cyclomatic number $cyc(G)$ of $G$ and maximum degree $\Delta(G)$ of $G$. We also give a sharp upper bound for the palette index of unicycle and bicycle graphs.
Keywords: edge coloring, bicycle graph.
Mots-clés : Palette, unicycle graph 
@article{UZERU_2019_53_1_a0,
     author = {A. V. Ghazaryan},
     title = {On the palette index of unicycle and bicycle graphs},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a0/}
}
TY  - JOUR
AU  - A. V. Ghazaryan
TI  - On the palette index of unicycle and bicycle graphs
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2019
SP  - 3
EP  - 12
VL  - 53
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a0/
LA  - en
ID  - UZERU_2019_53_1_a0
ER  - 
%0 Journal Article
%A A. V. Ghazaryan
%T On the palette index of unicycle and bicycle graphs
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2019
%P 3-12
%V 53
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a0/
%G en
%F UZERU_2019_53_1_a0
A. V. Ghazaryan. On the palette index of unicycle and bicycle graphs. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a0/