The planar Ramsey number for C4 and K5 is 13
نویسندگان
چکیده
منابع مشابه
A 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 کاملThe Ramsey Number r(K5-P3,K5)
For two given graphs G1 and G2, the Ramsey number r(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Km denote a complete graph of order m and Kn −P3 a complete graph of order n without two incident edges. In this paper, we prove that r(K5 − P3,K5) = 25 without help of computer algorithms.
متن کاملThe planar Ramsey number PR(K4-e, K5)
The planar Ramsey number PR (H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a copy of H2. It is known that the Ramsey number R(K4 − e, K6) = 21, and the planar Ramsey numbers PR(K4 − e, Kl) for l ≤ 5 are known. In this paper, we give the lower bounds on PR (K4 − e, Kl) and determine the exact value of PR (K4 − e, K6).
متن کاملComputation of the Ramsey Number R(W5,K5)
We determine the value of the Ramsey number R(W5, K5) to be 27, where W5 = K1 + C4 is the 4-spoked wheel of order 5. This solves one of the four remaining open cases in the tables given in 1989 by George R. T. Hendry, which included the Ramsey numbers R(G, H) for all pairs of graphs G and H having five vertices, except seven entries. In addition, we show that there exists a unique up to isomorp...
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 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00429-5