Decomposition of complete bipartite graphs into paths and stars with same number of edges

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Abstract

In this paper, we give some necessary and sufficient conditions for decomposing the complete bipartite graph Km, n into paths P k+1 and stars Sk+1 with k edges each. In particular, we find necessary and sufficient conditions for accomplishing this when m > k and n ≥ 3k, and we give a complete solution when k = 3. We also apply the results to show that for nonnegative integers p and q and positive integers n and k with n ≥ 4k, there exists a decomposition of the complete graph Kn into p copies of Pk+1 and q copies of Sk+ 1 if and only if k(p + q) = (n2).

Original languageEnglish
Pages (from-to)865-871
Number of pages7
JournalDiscrete Mathematics
Volume313
Issue number7
DOIs
Publication statusPublished - 2013 Apr 6
Externally publishedYes

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Keywords

  • Complete bipartite graph
  • Complete graph
  • Decomposition
  • Path
  • Star

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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