Let $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3-edge-coloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3-
edge-coloring of G can have is called the edge-coloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edge-coloring degree and, in particul...
Let $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3-edge-coloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3-
edge-coloring of G can have is called the edge-coloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edge-coloring degree and, in particula.r, when
G is c-critical, that is $d(G) = c \ge 1$ and $d(G - e) < c$ for any
edge $e$ of $G$.
Citation
Fiol, M. c-Critical graphs with maximum degree three. A: "Graph Theory, Combinatorics, and Applications". New York: John Wiley and Sons, Inc., 1995, p. 403-411.
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