All Ramsey Numbers r(K3, G) for Connected Graphs of Order 7 and 8

نویسنده

  • Gunnar Brinkmann
چکیده

In this paper we will give all Ramsey numbers r(K 3 ; G) for connected graphs G of order 7 and 8. For smaller orders and not connected graphs of order up to 8, the number of graphs with given Ramsey number is listed for all possible values.

برای دانلود 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

All Ramsey numbers r ( K 3 , G ) for connected graphs of order 9 Stephan Brandt

We determine the Ramsey numbers r(K3, G) for all 261080 connected graphs of order 9 and further Ramsey numbers of this type for some graphs of order up to 12. Almost all of them were determined by computer programs which are based on a program for generating maximal triangle-free graphs.

متن کامل

All Ramsey Numbers $r(K_3, G)$ For Connected Graphs of Order 9

We determine the Ramsey numbers r(K3, G) for all 261080 connected graphs of order 9 and further Ramsey numbers of this type for some graphs of order up to 12. Almost all of them were determined by computer programs which are based on a program for generating maximal triangle-free graphs.

متن کامل

The Ramsey numbers of large trees versus wheels

For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.

متن کامل

Ramsey Numbers R(K3, G) for Graphs of Order 10

In this article we give the generalized triangle Ramsey numbers R(K3, G) of 12 005 158 of the 12 005 168 graphs of order 10. There are 10 graphs remaining for which we could not determine the Ramsey number. Most likely these graphs need approaches focusing on each individual graph in order to determine their triangle Ramsey number. The results were obtained by combining new computational and th...

متن کامل

All 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 کامل

ذخیره در منابع من


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

برای دانلود 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

عنوان ژورنال:
  • Combinatorics, Probability & Computing

دوره 7  شماره 

صفحات  -

تاریخ انتشار 1998