Proof of a Conjecture of Bollobás and Eldridge for Graphs of Maximum Degree Three*

Let G 1 and G 2 be simple graphs on n vertices. If there are edge-disjoint copies of G 1 and G 2 in K n , then we say there is a packing of G 1 and G 2. A conjecture of Bollobás and Eldridge [5] asserts that if (Δ(G 1)+1) (Δ(G 2)+1) ≤ n + 1 then there is a packing of G 1 and G 2. We prove this conjecture when Δ(G 1) = 3, for sufficiently large n.

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Correspondence to Béla Csaba†‡.

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* This work was supported in part by a grant from National Science Foundation (DMS-9801396).

† Partially supported by OTKA T034475.

‡ Part of this work was done while the authors were graduate students at Rutgers University; Research partially supported by a DIMACS fellowship.

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Csaba†‡, B., Shokoufandeh‡, A. & Szemerédi, E. Proof of a Conjecture of Bollobás and Eldridge for Graphs of Maximum Degree Three*. Combinatorica 23, 35–72 (2003). https://doi.org/10.1007/s00493-003-0013-4

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AMS Subject Classification (2000):

  • 05C35
  • 05C70