Browsing by Subject "edge coloring"

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Access status: Open Access ,
A note on M2-edge colorings of graphs
(2015) Czap, Július
An edge coloring $\varphi$ of a graph $G$ is called an $M_2$-edge coloring if $|\varphi(v)|\le2$ for every vertex $v$ of $G$, where $\varphi(v)$ is the set of colors of edges incident with $v$. Let $K_{2}(G)$ denote the maximum number of colors used in an $M_2$-edge coloring of $G$. Let $G_1$, $G_2$ and $G_3$ be graphs such that $G_1\subseteq G_2\subseteq G_3$. In this paper we deal with the following question: Assuming that $K_2(G_1)=K_2(G_3)$, does it hold $K_2(G_1)=K_2(G_2)=K_2(G_3)$?
Access status: Restricted ,
Liczba paletowa grafu
(Data obrony: 2012-10-18) Frączek, Magdalena
Wydział Matematyki Stosowanej
Access status: Open Access ,
M₂-edge colorings of dense graphs
(2016) Ivančo, Jaroslav
An edge coloring $\varphi$ of a graph $G$ is called an $\mathrm{M}_i$-edge coloring if $|\varphi(v)|\leq i$ for every vertex $v$ of $G$, where $\varphi(v)$ is the set of colors of edges incident with $v$. Let $\mathcal{K}_i(G)$ denote the maximum number of colors used in an $\mathrm{M}_i$-edge coloring of $G$. In this paper we establish some bounds of $\mathcal{K}_2(G)$, present some graphs achieving the bounds and determine exact values of $\mathcal{K}_2(G)$ for dense graphs.
Access status: Restricted ,
Ogólne kolorowanie rozróżniające sąsiadów
(Data obrony: 2009-07-01) Firek, Sabina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Silne kolorowania krawędziowe grafów
(Data obrony: 2013-10-30) Koniecka, Żaneta
Wydział Matematyki Stosowanej