On a graph packing conjecture by Bollobás, Eldridge and Catlin
نویسندگان
چکیده
Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets are disjoint. In 1978, Bollobás and Eldridge, and independently Catlin, conjectured that if (∆(G1)+1)(∆(G2)+1)≤ n+1, then G1 and G2 pack. Towards this conjecture, we show that for ∆(G1),∆(G2)≥ 300, if (∆(G1)+1)(∆(G2)+1)≤0.6n+1, then G1 and G2 pack. This is also an improvement, for large maximum degrees, over the classical result by Sauer and Spencer that G1 and G2 pack if ∆(G1)∆(G2)<0.5n.
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ورودعنوان ژورنال:
- Combinatorica
دوره 28 شماره
صفحات -
تاریخ انتشار 2008