scholarly journals A Ramsey-type theorem for multiple disjoint copies of induced subgraphs

2014 ◽  
Vol 34 (2) ◽  
pp. 249
Author(s):  
Tomoki Nakamigawa
Keyword(s):  
Type Theorem ◽  
Induced Subgraphs ◽  
Ramsey Type

scholarly journals A Ramsey-Type Theorem in the Plane

1994 ◽  
Vol 3 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Jaroslav Nešetřil ◽  
Pavel Valtr
Keyword(s):  
Convex Hull ◽  
Type Theorem ◽  
Finite Set ◽  
Ramsey Type

We show that, for any finite set P of points in the plane and for any integer k ≥ 2, there is a finite set R = R(P, k) with the following property: for any k-colouring of R there is a monochromatic set , ⊆ R, such that is combinatorially equivalent to the set P, and the convex hull of P contains no point of R \ . We also consider related questions for colourings of p-element subsets of R (p > 1), and show that these analogues have negative solutions.

scholarly journals A Ramsey-type theorem for traceable graphs

1982 ◽  
Vol 33 (1) ◽  
pp. 7-16 ◽  
Author(s):  
F Galvin ◽  
I Rival ◽  
B Sands
Keyword(s):  
Type Theorem ◽  
Ramsey Type

A Ramsey-type theorem for the matching number regarding connected graphs

2020 ◽  
Vol 343 (2) ◽  
pp. 111648
Author(s):  
Ilkyoo Choi ◽  
Michitaka Furuya ◽  
Ringi Kim ◽  
Boram Park
Keyword(s):  
Type Theorem ◽  
Matching Number ◽  
Connected Graphs ◽  
Ramsey Type

Ramsey-Type Theorem for Spatial Graphs

1998 ◽  
Vol 14 (1) ◽  
pp. 75-80 ◽  
Author(s):  
Seiya Negami
Keyword(s):  
Type Theorem ◽  
Spatial Graphs ◽  
Ramsey Type

scholarly journals Separation Choosability and Dense Bipartite Induced Subgraphs

2019 ◽  
Vol 28 (5) ◽  
pp. 720-732 ◽  
Author(s):  
Louis Esperet ◽  
Ross J. Kang ◽  
Stéphan Thomassé
Keyword(s):  
Minimum Degree ◽  
Bipartite Graphs ◽  
Independent Interest ◽  
List Size ◽  
Induced Subgraphs ◽  
Natural Class ◽  
Free Graph ◽  
Induced Subgraph ◽  
Restricted Form ◽  
Ramsey Type

AbstractWe study a restricted form of list colouring, for which every pair of lists that correspond to adjacent vertices may not share more than one colour. The optimal list size such that a proper list colouring is always possible given this restriction, we call separation choosability. We show for bipartite graphs that separation choosability increases with (the logarithm of) the minimum degree. This strengthens results of Molloy and Thron and, partially, of Alon. One attempt to drop the bipartiteness assumption precipitates a natural class of Ramsey-type questions, of independent interest. For example, does every triangle-free graph of minimum degree d contain a bipartite induced subgraph of minimum degree Ω(log d) as d→∞?

A Ramsey-Type Theorem for Orderings of a Graph

1989 ◽  
Vol 2 (3) ◽  
pp. 402-406 ◽  
Author(s):  
Vojtech Rödl ◽  
Peter Winkler
Keyword(s):  
Type Theorem ◽  
Ramsey Type
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