Minimal path decomposition of complete bipartite graphs

This paper deals with the subject of minimal path decomposition of complete bipartite graphs. A path decomposition of a graph is a decomposition of it into simple paths such that every edge appears in exactly one path. If the number of paths is the minimum possible, the path decomposition is called...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 35; no. 3; pp. 684 - 702
Main Authors Constantinou, Costas K., Ellinas, Georgios
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2018
Springer Nature B.V
Subjects
Combinatorics
Convex and Discrete Geometry
Decomposition
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Graphs
Complete bipartite graphs
Decomposition algorithms
Minimal path decomposition
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ISSN1382-6905
1573-2886
1573-2886
DOI10.1007/s10878-017-0200-7

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Summary:This paper deals with the subject of minimal path decomposition of complete bipartite graphs. A path decomposition of a graph is a decomposition of it into simple paths such that every edge appears in exactly one path. If the number of paths is the minimum possible, the path decomposition is called minimal. Algorithms that derive such decompositions are presented, along with their proof of correctness, for the three out of the four possible cases of a complete bipartite graph.
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ISSN:1382-6905
1573-2886
1573-2886
DOI:10.1007/s10878-017-0200-7