The Ramsey Number r(K5-P3,K5)

نویسنده

  • Luis Boza
چکیده

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.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computing the Ramsey Number $R(K_5-P_3,K_5)$

We give a computer-assisted proof of the fact that R(K5 − P3,K5) = 25. This solves one of the three remaining open cases in Hendry’s table, which listed the Ramsey numbers for pairs of graphs on 5 vertices. We find that there exist no (K5−P3,K5)-good graphs containing a K4 on 23 or 24 vertices, where a graph F is (G, H)-good if F does not contain G and the complement of F does not containH. The...

متن کامل

Ramsey numbers for small graphs versus small disconnected graphs

The Ramsey number r(G,H) is determined for all disconnected (isolatefree) graphs H of order six and all graphs G of order at most five, except the three cases (G,H) ∈ {(K5 − 2K2, 2K3), (K5 − e, 2K3), (K5, 2K3)} where bounds with difference 1 are established. Moreover, general results are obtained for some small disconnected graphs H and any graph G.

متن کامل

Computation 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 کامل

Phase transitions in the Ramsey-Turán theory

Let f(n) be a function and L be a graph. Denote by RT(n, L, f(n)) the maximum number of edges of an L-free graph on n vertices with independence number less than f(n). Erdős and Sós [1] asked if RT(n,K5, c √ n) = o(n) for some constant c. We answer this question by proving the stronger RT ( n,K5, o (√ n log n )) = o(n). It is known that RT ( n,K5, c √ n log n ) = n/4 + o(n) for c > 1, so one ca...

متن کامل

Remarks on 15-vertex (3, 3)-Ramsey graphs not containing K5

The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K5 and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K4-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not cont...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 18  شماره 

صفحات  -

تاریخ انتشار 2011