The circular chromatic index of graphs of high girth
نویسندگان
چکیده
منابع مشابه
The circular chromatic index of graphs of high girth
We show that for each ε > 0 and each integer ∆ ≥ 1, there exists a number g such that for any graph G of maximum degree ∆ and girth at least g, the circular chromatic index of G is at most ∆ + ε.
متن کاملCircular Chromatic Number of Planar Graphs of Large Odd Girth
It was conjectured by Jaeger that 4k-edge connected graphs admit a (2k + 1, k)-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least 4k have circular chromatic number at most 2 + 1 k . Even this restricted version of Jaeger’s conjecture is largely open. The k = 1 case is the well-known Grötzsch 3-colour theorem. This paper ...
متن کاملSkew Chromatic Index of Circular Ladder Graphs
Abstract. A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, an algorithm is determined for skew edge coloring of circular ladder graphs. Alsothe skew chromatic index of circular la...
متن کاملStrong chromatic index of planar graphs with large girth
Let ∆ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree ∆ and girth at least 10∆+46 is strong (2∆−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of degree ∆. This improves [6] when ∆ ≥ 6.
متن کاملThe distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.03.002