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- W348664309 abstract "In this thesis, we study four problems in graph theory, the Hamiltonian cycle problem in line graphs, the edge-fault-tolerant bipancyclicity of Cayley graphs generated by transposition trees, the vertex-distinguishing arc colorings in digraph- s and the acyclic arc coloring in digraphs. The first two problems are the classic problem on the cycles in graphs. And the other two arc coloring problems are related to the modern graph theory, in which we use some probabilistic methods. In particular,We first study the Hamiltonian cycle problem in line graphs and find the Hamiltonian cycles in some spanning subgraphs of line graphs SL(G). We prove that: if L(G) is Hamiltonian, then SL(G) is Hamiltonian. Due to this, we propose a conjecture, which is equivalent to some well-known conjectures. And we get two results about the edge-disjoint Hamiltonian cycles in line graphs.Then, we consider the edge-fault-tolerant bipancyclicity of Cayley graphs generated by transposition trees. And we prove that the Cayley graph generated by transposition tree is (n − 3)-edge-fault-tolerant bipancyclic if it is not a star graph.Later, we introduce the vertex-distinguishing arc coloring in digraphs. We study the relationship between the vertex-distinguishing edge coloring in undirected graphs and the vertex-distinguishing arc coloring in digraphs. And we get some results on the (semi-) vertex-distinguishing arc chromatic number for digraphs and also propose a conjecture about it. To verify the conjecture we study the vertex-distinguishing arc coloring for regular digraphs.Finally, we introduce the acyclic arc coloring in digraphs. We calculate the acyclic arc chromatic number for some digraph families and propose a conjecture on the acyclic arc chromatic number. Then we consider the digraphs with high girth by using the Lovasz Local Lemma and we also consider the random regular digraphs. And the results of the digraphs with high girth and the random regular digraphs verify the conjecture." @default.
- W348664309 created "2016-06-24" @default.
- W348664309 creator A5040020968 @default.
- W348664309 date "2014-11-28" @default.
- W348664309 modified "2023-09-23" @default.
- W348664309 title "Cycles in graphs and arc colorings in digraphs" @default.
- W348664309 hasPublicationYear "2014" @default.
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