Abstract
A (3, 4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose components are nontrivial paths. We prove that a simple (3,4)-biregular bigraph always has a path factor such that the endpoints of each path have degree three. Moreover we suggest a polynomial algorithm for the construction of such a path factor.
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Asratian, A.S., Casselgren, C.J. On Path Factors of (3, 4)-Biregular Bigraphs. Graphs and Combinatorics 24, 405–411 (2008). https://doi.org/10.1007/s00373-008-0803-y
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DOI: https://doi.org/10.1007/s00373-008-0803-y