منابع مشابه
On a graph packing conjecture by Bollobás, Eldridge and Catlin
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 ...
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The Gyárfás tree packing conjecture states that any set of n−1 trees T1, T2, . . . , Tn−1 such that Ti has n− i+ 1 vertices pack into Kn (for n large enough). We show that t = 1 10n 1/4 trees T1, T2, . . . , Tt such that Ti has n− i+ 1 vertices pack into Kn+1 (for n large enough). We also prove that any set of t = 1 10 n1/4 trees T1, T2, . . . , Tt such that no tree is a star and Ti has n− i+ 1...
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The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined in terms of complexity classes such as P and EXP. For instance, GP denotes the class of graph classes that have a labeling scheme with a polynomial-time com...
متن کاملHadwiger’s Conjecture and Seagull Packing
T he four-color theorem [1, 2] is one of the most well-known results in graph theory. Originating from the question of coloring a world map, posed in the middle of the nineteenth century, it has since fascinated hundreds of researchers and motivated a lot of beautiful mathematics. It states that every planar graph (that is, a graph that can be drawn in the plane without crossings) can be proper...
متن کاملGraph packing with constraints on edges
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2016
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2016.v7.n2.a6