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- W755952011 abstract "In this thesis, we study arc colorings and cycles in digraphs. The following topics are considered: vertex-distinguishing proper arc colorings in digraphs, short cycles in digraphs with forbidden subgraphs , disjoint cycles in bipartite tournaments, cycle factors in regualr bipartite tournaments and universal arcs in tournaments. The main results are contained in five original articles published or submitted to an international journal. We introduce vertex-distinguishing proper arc colorings of digraphs. A conjecture on the vertex-distinguishing arc-chromatic number is given and some partial results are obtained. We extend a result of Razborov by proving that the Caccetta-Haggkvist conjecture is true for digraphs with certain induced forbidden subgraphs or with certain forbidden subgraphs. We show that every bipartite tournament with minimum outdegree at least qr-1 has r vertex disjoint cycles of any given possible lengths. The special case q=2 of the result verifies the bipartite tournament case of the Bermond-Thomassen conjecture. As a partial support of a conjecture on 2-cycle-factors in bipartite tournaments, we prove that every k-regular bipartite tournament B with k>2 has two complementary cycles of lengths 6 and |V(B)|-6, unless B is isomorphic to a special digraph. Besides, we show that every k-connected regular bipartite tournament has a k-cycle-factor. We also give a sufficient and necessary condition for the existence of a universal arc in a tournament and characterize all the tournaments in which every arc is universal." @default.
- W755952011 created "2016-06-24" @default.
- W755952011 creator A5065163044 @default.
- W755952011 date "2014-11-28" @default.
- W755952011 modified "2023-09-27" @default.
- W755952011 title "Arc colorings and cycles in digraphs" @default.
- W755952011 hasPublicationYear "2014" @default.
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