On the chromatic index of path decompositions
نویسندگان
چکیده
منابع مشابه
On the chromatic index of path decompositions
If G = (V ′, E) is a graph and H = (V,H) is a graph whose edges can be decomposed into isomorphic copies of G, then we define a k-block colouring of a G−decomposition of H to be an assignment of k colours to the copies of G so that no two copies of G having a vertex in common have the same colour. A G−decomposition of H has chromatic index χ′ = k if it is k block colourable and not k − 1 block ...
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Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let Gk be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai’s conjecture holds in Gk, for every k ≥ 3. Further, we prove that for every graph G in Gk on n vertices, there exists a par...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.11.027