Packing degenerate graphs
نویسندگان
چکیده
منابع مشابه
Packing d-degenerate graphs
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobás–Eldridge–Catlin conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d,∆1,∆2 ≥ 1 and n > max{40∆1 ln ∆2, 40d∆2} then a d-degenerate graph of maximal degree ∆1 and a graph of order n and maximal degree ∆2 pack. We use this result to ...
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We prove that if G is a family of graphs with at most n vertices each, with constant degeneracy, with maximum degree at most O (n/ logn), and with total number of edges at most (1 − o(1)) (n 2 ) , then G packs into the complete graph Kn. This strengthens recent results of Böttcher Hladký Piguet Taraz, Messuti Rödl Schacht, Ferber Lee Mousset, Kim Kühn Osthus Tyomkyn, and Ferber Samotij related ...
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In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.
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in a graph g = (v,e), a subset s v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.
متن کاملPacking Graphs: The packing problem solved
Abstract For every fixed graph H, we determine the H-packing number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, P (H, Kn) = b 2h b n − 1 d cc, unless n = 1 mod d and n(n − 1)/d = b mod (2h/d) where 1 ≤ b ≤ d, in which case P (H, Kn) = b 2h b n ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2019
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106739