Journal Article10.1017/S0963548300000663
Ramsey Problems with Bounded Degree Spread
Guantao Chen,Richard H. Schelp +1 more
13
TL;DR: In this paper, the authors studied bipartite graphs G such that, for n sufficiently large, each two-coloring of the edges of the complete graph Kn gives a monochromatic copy of G, with some k of its vertices having the maximum degree of these k vertices minus the minimum degree of the vertices (in the colored Kn) at most k − 2.
read more
Abstract: Let k be a positive integer, k ≥ 2. In this paper we study bipartite graphs G such that, for n sufficiently large, each two-coloring of the edges of the complete graph Kn gives a monochromatic copy of G, with some k of its vertices having the maximum degree of these k vertices minus the minimum degree of these k vertices (in the colored Kn) at most k − 2.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Generalizing the Ramsey Problem through Diameter
TL;DR: The results include determining $f_1^k(K_n)$, which is equivalent to determining classical Ramsey numbers for multicolorings, and a construction due to Calkin implies that $f-3^k (K-n) \le {{n}\over {k-1}} + k-1$ when $k- 1$ is a prime power.
Forcing $k$-Repetitions in Degree Sequences
TL;DR: It is shown that for any positive integer $k$, there is a constant $C=C(k)$, so that given any graph $G$, one can remove from $G$ at most $C$ vertices and thus obtain a new graph "$G'$ that contains at least $\min\{k,|G|-C\}$ Vertices of the same degree.
•Posted Content
Forcing $k$-repetitions in degree sequences
TL;DR: In this paper, it was shown that for any positive integer k, there is a constant k = C(k) where k is the number of vertices of the same degree in a graph.
8
•Posted Content
Singular Ramsey and Tur\'an numbers
Yair Caro,Zsolt Tuza +1 more
TL;DR: In this article, the singular Ramsey number is defined as the smallest positive integer such that, for every edge 2-coloring of a graph, at least one of the color classes contains a singular subgraph.
6
Singular Ramsey and Turán numbers
Yair Caro,Zsolt Tuza +1 more
- 01 Jan 2019
TL;DR: In this article, the singular Ramsey number is defined as the smallest positive integer such that, for every edge 2-coloring of a graph, at least one of the color classes contains a singular subgraph.
References
A problem of Zarankiewicz
TL;DR: This paper improves upon previously known upper bounds for kα,β(m, n) by proving that k αβ (m,n)⩾ 1+((β−1) ( p α−1 ))( m α ) + ((p+1)(α− 1) α )n for each integer p greater than or equal to α − 1.
116
Ramsey Problems Involving Degrees in Edge-colored Complete Graphs of Vertices Belonging to Monochromatic Subgraphs
TL;DR: This work considers monochromatic subragraphs in two-colored graphs as guaranteed by Ramsey's theorem, and asks various questions concerning the degree in the two- colored complete graphs of vertices which are part of these subgraphs.
24