منابع مشابه
Online Ramsey Theory for Planar Graphs
An online Ramsey game (G,H) is a game between Builder and Painter, alternating in turns. During each turn, Builder draws an edge, and Painter colors it blue or red. Builder’s goal is to force Painter to create a monochromatic copy of G, while Painter’s goal is to prevent this. The only limitation for Builder is that after each of his moves, the resulting graph has to belong to the class of grap...
متن کاملPlanar Ramsey Numbers for Small Graphs
Given two graphs G1 and G2, the planar Ramsey number PR(G1, G2) is the smallest integer n such that every planar graph on n vertices either contains a copy of G1 or its complement contains a copy of G2. So far, the planar Ramsey numbers have been determined, when both, G1 and G2 are complete graphs or both are cycles. By combining computer search with some theoretical results, in this paper we ...
متن کاملA note on the Ramsey number and the planar Ramsey number for C4 and complete graphs
We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
متن کاملAll Ramsey (2K2,C4)−Minimal Graphs
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...
متن کاملPlanar Ramsey Numbers
The planar Ramsey number PR(G, H) is defined as the smallest integer n for which any 2-colouring of edges of Kn with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8366