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

Authors:
Béla Csaba;Ali Shokoufandeh;Endre Szemerédi
Affiliations:
Max-Planck-Inst. für Informatik, Germany;Drexel University, Dept. of Computer Science, USA;Rutgers University, Dept. of Computer Science, USA
Venue:
Combinatorica
Year:
2003

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Abstract

Let G1 and G2 be simple graphs on n vertices. If there are edge-disjoint copies of G1 and G2 in Kn, then we say there is a packing of G1 and G2. A conjecture of Bollobás and Eldridge [5] asserts that if (Δ(G1)+1) (Δ(G2)+1) ≤ n + 1 then there is a packing of G1 and G2. We prove this conjecture when Δ(G1) = 3, for sufficiently large n.