The integer sequence A002620 and upper antagonistic functions.
Speed, Sam E. (2003)
Journal of Integer Sequences [electronic only]
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Speed, Sam E. (2003)
Journal of Integer Sequences [electronic only]
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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...
Faudree, Jill R., Faudree, Ralph J., Schmitt, John R. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Radziszowski, Stanisław P. (1996)
The Electronic Journal of Combinatorics [electronic only]
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Vladimír Puš (1987)
Commentationes Mathematicae Universitatis Carolinae
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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.
Brandt, Stephan, Brinkmann, Gunnar, Harmuth, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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Klazar, Martin (2000)
The Electronic Journal of Combinatorics [electronic only]
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Jair Donadelli, Penny E. Haxell, Yoshiharu Kohayakawa (2005)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Let be the graph obtained from a given graph by subdividing each edge 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 , there exist graphs with edges that are Ramsey with respect to .
Grytczuk, Jarosław (2007)
International Journal of Mathematics and Mathematical Sciences
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