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Arbitrary decompositions into open and closed trails
Authors:Sylwia Cichacz  Yoshimi Egawa
Affiliation:a Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
b Department of Mathematical Information Science, Tokyo University of Science, Japan
Abstract:The problem of arbitrary decomposition of a graph G into closed trails i.e. a decomposition into closed trails of prescribed lengths summing up to the size of the graph G was first considered in the case of the complete graph G=Kn (for odd n) in connection with vertex-distinguishing coloring of the union of cycles.Next, the same problem was investigated for other families of graphs.In this paper we consider a more general problem: arbitrary decomposition of a graph into open and closed trails. Our results are based on and generalize known results on decomposition of a graph into closed trails. Our results also generalize some results concerning decomposition of a graph into open trails. We here emphasize that the known results on the closed case are basic ingredients for the proof of the open and closed case.
Keywords:Decomposition   Trail
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