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Vertex-disjoint cycles in regular tournaments

✍ Scribed by Nicolas Lichiardopol


Book ID
113567635
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
210 KB
Volume
312
Category
Article
ISSN
0012-365X

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## Abstract Enomoto 7 conjectured that if the minimum degree of a graph __G__ of order __n__ β‰₯ 4__k__ βˆ’ 1 is at least the integer $ \left \lfloor \sqrt{n+\left (\,{9 \over 4}k^2 - 4k + 1\right)} \,+ {3 \over 2}k - 1 \right \rfloor$, then for any __k__ vertices, __G__ contains __k__ vertex‐disjoint

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We prove that any k-regular directed graph with no parallel edges contains a collection of at least fl(k2) edge-disjoint cycles; we conjecture that in fact any such graph contains a collection of at least ( lCi1 ) disjoint cycles, and note that this holds for k 5 3. o 1996