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Star-critical connected Ramsey numbers for 2-colorings of complete graphs [PDF]
Transactions on CombinatoricsThis paper builds upon Sumner's work by further investigating the concept of connected Ramsey numbers, specifically focusing on star-critical connected Ramsey numbers.
Monu Moun, Jagjeet Jakhar, Mark Budden
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Size Ramsey number of bipartite graphs and bipartite Ramanujan graphs [PDF]
Transactions on Combinatorics, 2019 Given a graph $ G $, a graph $ F $ is said to be Ramsey for $ G $ if in every edge coloring of $F$ with two colors, there exists a monochromatic copy of $G$. The minimum number of edges of a graph $ F $ which is Ramsey for $ G $ is called the size-Ramsey
Ramin Javadi, Farideh Khoeini
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Journal of Combinatorial Theory, Series B, 1993 The planar Ramsey number \(\text{PR}(k,\ell)\) \((k,\ell\geq 2)\) is the smallest integer \(n\) such that any planar graph on \(n\) vertices contains either a complete graph on \(k\) vertices or an independent set of size \(\ell\). We find exact values of \(\text{PR}(k,\ell)\) for all \(k\) and \(\ell\).
Steinberg, R., Tovey, C.A.
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Chromatic Ramsey number of acyclic hypergraphs [PDF]
, 2015 Suppose that $T$ is an acyclic $r$-uniform hypergraph, with $r\ge 2$. We define the ($t$-color) chromatic Ramsey number $\chi(T,t)$ as the smallest $m$ with the following property: if the edges of any $m$-chromatic $r$-uniform hypergraph are colored with
Gyárfás, András +2 more
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Degree Bipartite Ramsey Numbers [PDF]
Taiwanese Journal of Mathematics, 2021 Let $H\xrightarrow{s} G$ denote that any edge-coloring of $H$ by $s$ colors contains a monochromatic $G$. The degree Ramsey number $r_ (G;s)$ is defined to be $\min\{ (H):H\xrightarrow{s} G\}$, and the degree bipartite Ramsey number $br_ (G;s)$ is defined to be $\min\{ (H):H\xrightarrow{s} G\; \mbox{and} \; (H)=2\}$. In this note, we show that $r_
Wang, Ye, Li, Yusheng, Li, Yan
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Three-colour bipartite Ramsey number R_b(G_1,G_2,P_3)
Electronic Journal of Graph Theory and Applications, 2020 For simple bipartite graphs G1, G2, G3, the three-colour bipartite graph Ramsey number Rb(G1,G2,G3) is defined as the least positive integer n such that any 3-edge-colouring of Kn,n assures a monochromatic copy of Gi in the ith colour for some i, i ∈ {1 ...
R Lakshmi, D.G. Sindhu
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A note on the size Ramsey numbers for matchings versus cycles [PDF]
Mathematica Bohemica, 2021 For graphs $G$, $F_1$, $F_2$, we write $G \rightarrow(F_1, F_2)$ if for every red-blue colouring of the edge set of $G$ we have a red copy of $F_1$ or a blue copy of $F_2$ in $G$.
Edy Tri Baskoro, Tomáš Vetrík
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A note on the Ramsey number for cycle with respect to multiple copies of wheels
Electronic Journal of Graph Theory and Applications, 2021 Let Kn be a complete graph with n vertices. For graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that in every red-blue coloring on the edges of Kn, there is a red copy of graph G or a blue copy of graph H in Kn ...
I Wayan Sudarsana
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Large Book-Cycle Ramsey Numbers [PDF]
SIAM Journal on Discrete Mathematics, 2021 Let $B_n^{(k)}$ be the book graph which consists of $n$ copies of $K_{k+1}$ all sharing a common $K_k$, and let $C_m$ be a cycle of length $m$. In this paper, we first determine the exact value of $r(B_n^{(2)}, C_m)$ for $\frac{8}{9}n+112\le m\le \lceil\frac{3n}{2}\rceil+1$ and $n \geq 1000$.
Lin, Qizhong, Peng, Xing
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Multicolor Size-Ramsey Number of Paths
پژوهشهای ریاضی, 2021 The size-Ramsey number of a graph denoted by is the smallest integer such that there is a graph with edges with this property that for any coloring of the edges of with colors, contains a monochromatic copy of.
Ramin Javadi, Meysam Miralaei
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