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On avoiding and completing edge colorings

These papers are all related to the problem of avoiding and completing an edge precoloring of a graph. In more detail, given a graph G and a partial proper edge precoloring φ of G and a list assignment L for every non-colored edge of G, can we extend the precoloring to a proper edge coloring avoiding any list assignment? In the first paper, G is a d-dimensional hypercube graph Qd, a partial proper edge precoloring φ and every list assignment L must satisfy certain sparsity conditions. The second paper still deals with d-dimensional hypercube graph Qd, but the list assignment L for every edge of Qd is an empty set and φ must be a partial proper edge precoloring of at most (d - 1) edges. For the third paper, G can be seen as a complete 3-uniform 3-partite hypergraph, every list assignment L must satisfy certain sparsity conditions but we do not have a partial proper edge precoloring φ on edges of G.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-146915
Date January 2018
CreatorsPham, Lan Anh
PublisherUmeå universitet, Institutionen för matematik och matematisk statistik, Umeå : Umeå University
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeLicentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationResearch report in mathematics, 1653-0810

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