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Unbalanced Star-Factorizations of Complete Bipartite Graphs II

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Abstract

There are simple arithmetic conditions necessary for the complete bipartite graph Km,n to have a complete factorization by subgraphs which are made up of disjoint copies of Kp,q. It is conjectured that these conditions are also sufficient. In any factor the copies of Kp,q have two orientations depending which side of the bipartition the p-set lies. The balance ratio is the relative proportion, x:y of these where gcd(x,y)=1. In this paper, we continue the study of the unbalanced case (y > x) where p = 1, to show that the conjecture is true whenever y is sufficiently large. We also prove the conjecture for K1,4-factorizations.

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  1. Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, England

    Nigel Martin

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  1. Nigel Martin
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Correspondence to Nigel Martin.

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Martin, N. Unbalanced Star-Factorizations of Complete Bipartite Graphs II. Graphs and Combinatorics 23, 559–583 (2007). https://doi.org/10.1007/s00373-007-0753-9

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  • DOI: https://doi.org/10.1007/s00373-007-0753-9

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