Displaying similar documents to “On the Turán properties of infinite graphs.”

A ramsey-type theorem for multiple disjoint copies of induced subgraphs

Tomoki Nakamigawa (2014)

Discussiones Mathematicae Graph Theory

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Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to each other and they are isomorphic to one of four graphs: (1) a clique of order k, (2) an independent set of order k, (3) the join of a clique of order ℓ and an independent set of order k − ℓ, or (4) the union of an independent set of...

Small Ramsey numbers.

Radziszowski, Stanisław P. (1996)

The Electronic Journal of Combinatorics [electronic only]

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A Survey of the Path Partition Conjecture

Marietjie Frick (2013)

Discussiones Mathematicae Graph Theory

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The Path Partition Conjecture (PPC) states that if G is any graph and (λ1, λ2) any pair of positive integers such that G has no path with more than λ1 + λ2 vertices, then there exists a partition (V1, V2) of the vertex set of G such that Vi has no path with more than λi vertices, i = 1, 2. We present a brief history of the PPC, discuss its relation to other conjectures and survey results on the PPC that have appeared in the literature since its first formulation in 1981.

A note on the Size-Ramsey number of long subdivisions of graphs

Jair Donadelli, Penny E. Haxell, Yoshiharu Kohayakawa (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Let T s H be the graph obtained from a given graph H by subdividing each edge s times. Motivated by a problem raised by Igor Pak [Mixing time and long paths in graphs, in Proc. of the 13th annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002) 321–328], we prove that, for any graph H , there exist graphs G with O ( s ) edges that are Ramsey with respect to T s H .