Gallai’s path decomposition conjecture for graphs of small maximum degree
نویسندگان
چکیده
منابع مشابه
Gallai's path decomposition conjecture for graphs of small maximum degree
Gallai’s path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most n+1 2 paths. We confirm that conjecture for all graphs with maximum degree at most five.
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A path decomposition of a graph G is a collection of edge-disjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most ⌊(n + 1)/2⌋. Gallai’s Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex wi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.01.005