Minimum degree conditions for H-linked graphs
نویسندگان
چکیده
منابع مشابه
Minimum degree conditions for H-linked graphs
For a fixed multigraph H with vertices w1, . . . , wm, a graph G is H-linked if for every choice of vertices v1, . . . , vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs. Given a connected multigraph H with k edges and minimum degree at least two and n 7.5k, we...
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For a given multigraph H , a graph G is H-linked, if |G| ≥ |H| and for every injective map τ : V (H) → V (G), we can find internally disjoint paths in G, such that every edge from uv in H corresponds to a τ(u)− τ(v) path. To guarantee that a G is H-linked, you need a minimum degree larger than |G| 2 . This situation changes, if you know that G has a certain connectivity k. Depending on k, even ...
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Given a digraphH, anH-subdivision is any digraph obtained by replacing each arc uv of H with a (directed) u− v path of arbitrary length. A directed graph D is H-linked if every injective functionf : V (H) → V (D) extends to an H-subdivision in G. The H-linkage property has been well-studied in undirected graphs, and in both the directed and undirected case generalizes the notions of k-linked an...
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For a k-linked graph G and a vector E S of 2k distinct vertices of G, an E S-linkage is a set of k vertex-disjoint paths joining particular vertices of E S. Let T denote theminimum order of an E S-linkage in G. A graph G is said to be pan-k-linked if it is k-linked and for all vectors E S of 2k distinct vertices of G, there exists an E S-linkage of order t for all t such that T ≤ t ≤ |V (G)|. W...
متن کاملH-Free Graphs of Large Minimum Degree
We prove the following extension of an old result of Andrásfai, Erdős and Sós. For every fixed graph H with chromatic number r+1 ≥ 3, and for every fixed > 0, there are n0 = n0(H, ) and ρ = ρ(H) > 0, such that the following holds. Let G be an H-free graph on n > n0 vertices with minimum degree at least ( 1 − 1 r−1/3 + ) n. Then one can delete at most n2−ρ edges to make G r-colorable.
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2005
ISSN: 1571-0653
DOI: 10.1016/j.endm.2005.07.070