Results 11 to 20 of about 21,746 (178)

On the path-complete bipartite Ramsey number

Discrete Mathematics, 1989
Publisher Summary Let r(P k , K n,m ) denote the (mixed) Ramsey number between a path Pk on k vertices and a K n,m . Thus r(P k , K n,m ) is the minimal number such that every graph G on r(P k , K n,m ) vertices either contains a Pk, or else contains a K n,m in the complement G. The chapter proves the theorem r(P k , K n ,m ) ≤ n
R. Häggkvist
semanticscholar   +2 more sources

3‐Color bipartite Ramsey number of cycles and paths [PDF]

Journal of Graph Theory, 2018
The k ‐color bipartite Ramsey number of a bipartite graph H is the least integer n for which every k ‐edge‐colored complete bipartite graph Kn,n contains a monochromatic copy of H .
M. Buci'c, Shoham Letzter, B. Sudakov
semanticscholar   +4 more sources

The Bipartite $K_{2, 2}$-Free Process and Bipartite Ramsey Number $b(2, t)$ [PDF]

The Electronic Journal of Combinatorics, 2018
The bipartite Ramsey number $b(s,t)$ is the smallest integer $n$ such that every blue-red edge coloring of $K_{n,n}$ contains either a blue $K_{s,s}$ or a red $K_{t,t}$. In the bipartite $K_{2,2}$-free process, we begin with an empty graph on vertex set $
Deepak Bal, Patrick Bennett
semanticscholar   +5 more sources

Bipartite Ramsey Numbers for Graphs of Small Bandwidth

The Electronic Journal of Combinatorics, 2018
A graph $H=(W,E_H)$ is said to have bandwidth  at most $b$ if there exists a labeling of $W$ as $w_1,w_2,\dots,w_n$ such that $|i-j|\leq b$ for every edge $w_iw_j\in E_H$, and a bipartite balanced $(\beta,\Delta)$-graph  $H$ is a bipartite graph with ...
Lili Shen, Qizhong Lin, Qinghai Liu
semanticscholar   +3 more sources

Three-Color Bipartite Ramsey Number for Graphs with Small Bandwidth

SIAM Journal on Discrete Mathematics, 2018
We estimate the $3$-colour bipartite Ramsey number for balanced bipartite graphs $H$ with small bandwidth and bounded maximum degree. More precisely, we show that the minimum value of $N$ such that in any $3$-edge colouring of $K_{N,N}$ there is a ...
G. Mota
semanticscholar   +3 more sources

Insect visitation patterns in diploid Centaurea aspera and its related allotetraploid and triploid hybrids: Similar rates but distinct assemblages. [PDF]

Am J Bot
Abstract Premise Polyploidy is key to plant evolution by contributing to speciation, diversification, and adaptability. However, the minority cytotype exclusion effect can limit the persistence of polyploids, which can be mitigated by reproductive barriers such as distinct insect visitation between cytotypes. In eastern Spain, the diploid C.
Garmendia A, Merle H, Lucio-Puig P, Ferriol M.   +3 more
europepmc   +2 more sources

New values for the bipartite Ramsey number of the four-cycle versus stars

Discrete Mathematics, 2021
We provide new values of the bipartite Ramsey numberRB(C4,K1,n) using induced subgraphs of the incidence graph of a projective plane. The approach, based on deleting subplanes of projective planes, has been used in related extremal problems and allows us
Imre Hatala, Tamás Héger, Sam Mattheus
semanticscholar   +1 more source

Asymptotic Bounds for Bipartite Ramsey Numbers [PDF]

The Electronic Journal of Combinatorics, 2001
The bipartite Ramsey number $b(m,n)$ is the smallest positive integer $r$ such that every (red, green) coloring of the edges of $K_{r,r}$ contains either a red $K_{m,m}$ or a green $K_{n,n}$. We obtain asymptotic bounds for $b(m,n)$ for $m \geq 2$ fixed and $n \rightarrow \infty$.
Caro, Yair, Rousseau, Cecil
openaire   +2 more sources

Ramsey sequences of graphs

AKCE International Journal of Graphs and Combinatorics, 2020
A sequence of graphs is a Ramsey sequence if for every positive integer k, the graph Gk is isomorphic to a proper subgraph of and for each positive integer k, there is an integer such that every red-blue coloring of Gn results in a monochromatic Gk. Some
Gary Chartrand, Ping Zhang
doaj   +1 more source

Bipartite rainbow Ramsey numbers

Discrete Mathematics, 2004
This article introduces, proves the existence of, and computes some values of a new Ramsey number. Given a graph \(G\), with a subgraph \(H\), call an edge-coloring of \(G\) {rainbow} on \(H\) if the coloring assigns every edge of \(H\) its own color.
Eroh, Linda, Oellermann, Ortrud R.
openaire   +2 more sources