On the minimum degree of minimal Ramsey graphs for multiple colours

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the minimum degree of minimal Ramsey graphs for multiple colours

A graph G is r-Ramsey for a graph H, denoted by G→ (H)r, if every r-colouring of the edges of G contains a monochromatic copy of H. The graph G is called r-Ramseyminimal for H if it is r-Ramsey for H but no proper subgraph of G possesses this property. Let sr(H) denote the smallest minimum degree of G over all graphs G that are r-Ramseyminimal for H. The study of the parameter s2 was initiated ...

متن کامل

The minimum degree of Ramsey-minimal graphs

We write H → G if every 2-coloring of the edges of graph H contains a monochromatic copy of graph G. A graph H is G-minimal if H → G, but for every proper subgraph H ′ of H, H ′ 6→ G. We define s(G) to be the minimum s such that there exists a G-minimal graph with a vertex of degree s. We prove that s(Kk) = (k − 1) and s(Ka,b) = 2 min(a, b) − 1. We also pose several related open problems. c © 2...

متن کامل

On the minimum degree of minimal Ramsey graphs

We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr, Erdős, and Lovász. We determine the corresponding graph parameter for numerous bipartite graphs, including bi-regular bipartite graphs and forests. We also make initial progress for graphs of larger chromatic number. Numerous interesting problems remain open.

متن کامل

Minimum Degrees of Minimal Ramsey Graphs

For graphs F and H, we say F is Ramsey for H if every 2-coloring of the edges of F contains a monochromatic copy of H. The graph F is Ramsey H-minimal if there is no proper subgraph F ′ of F so that F ′ is Ramsey for H. Burr, Erdős, and Lovász defined s(H) to be the minimum degree of F over all Ramsey H-minimal graphs F . Define Ht,d to be a graph on t+ 1 vertices consisting of a complete graph...

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

ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series B

سال: 2016

ISSN: 0095-8956

DOI: 10.1016/j.jctb.2016.03.006