Graph packing with constraints on edges
نویسنده
چکیده
A graph consists of a set of vertices (nodes) and a set of edges (line connecting vertices). Two graphs pack when they have the same number of vertices and we can put them in the same vertex set without overlapping edges. Studies such as Sauer and Spencer [7], Bollobás and Eldridge [1], Kostochka and Yu [6], have shown sufficient conditions, specifically relations between number of edges in the two graphs, for two graphs to pack, but only a few addressed packing with constraints. Kostochka and Yu [6] proved that if e1e2 < (1−ε)n2, then G1 and G2 pack with exceptions. We extend this finding by using the language of list packing introduced by Győri, Kostochka, McConvey, and Yager [2], and we show that the triple (G1, G2, G3) with e1e2 + n−1 2 · e3 < (2− ε) ( n 2 ) pack with well-defined exceptions.
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