منابع مشابه
H-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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A graph G is called C4-free if it does not contain the cycle C4 as an induced subgraph. Hubenko, Solymosi and the first author proved (answering a question of Erdős) a peculiar property of C4-free graphs: C4 graphs with n vertices and average degree at least cn contain a complete subgraph (clique) of size at least c′n (with c′ = 0.1c2n). We prove here better bounds (c2n/3 in general and (c− 1/3...
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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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The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
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We consider the H-coloring problem on graphs with vertices of large degree. We prove that for H an odd cycle, the problem belongs to P. We also study the phase transition of the problem, for an infinite family of graphs of a given chromatic number, i.e. the threshold density value for which the problem changes from P to NP-complete. We extend the result for the case that the input graph has a l...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1045