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Decomposition of Regular Bipartite Graphs Into Hamiltonian Cycles (Paths) and S3

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  • V. Nalini
  • S. Jeevadoss

Abstract

Let G be either a complete bipartite graph with n (even) vertices in each partite or a complete bipartite graph with n (odd) vertices in each partite plus a 1‐factor. A Hamiltonian cycle (respectively, path) of G is a cycle (respectively, path) that visits each vertex exactly once. In this paper, we determine the necessary and sufficient conditions for decomposing the graph G into λ copies of Hamiltonian cycles (or paths) and μ copies of the S3, a star with three edges if and only if n2 + εn = 2nλ + 3μ(or n2 + εn = (2n − 1)λ + 3μ), where ε = 1 if n is odd and ε = 0 if n is even.

Suggested Citation

  • V. Nalini & S. Jeevadoss, 2025. "Decomposition of Regular Bipartite Graphs Into Hamiltonian Cycles (Paths) and S3," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:2349979
    DOI: 10.1155/jom/2349979
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    References listed on IDEAS

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    1. Yilun Shang, 2015. "On the Hamiltonicity of random bipartite graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 163-173, April.
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