Results 51 to 60 of about 21,746 (178)
Extremal theory and bipartite graph-tree Ramsey numbers
Discrete Mathematics, 1988 The authors contribute to the extremal Ramsey theory on graphs. In particular Ramsey numbers for trees and bipartite graphs are upperbounded. Tecnical mechanism developed for proving the main result is interesting in its own right and seems to be useful for further researches.
Erd'́os, P. +3 more
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A Sharper Ramsey Theorem for Constrained Drawings
Journal of Graph Theory, Volume 109, Issue 4, Page 401-411, August 2025.ABSTRACT Given a graph G and a collection C of subsets of R d indexed by the subsets of vertices of G, a constrained drawing of G is a drawing where each edge is drawn inside some set from C, in such a way that nonadjacent edges are drawn in sets with disjoint indices. In this paper we prove a Ramsey‐type result for such drawings.
Pavel Paták
wiley +1 more source
Multicolor bipartite Ramsey number of double stars
, 2023 For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. Finding monochromatic copies of double stars in edge-colored complete bipartite graphs has attracted much attention.
DeCamillis, Gregory, Song, Zi-Xia
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Canonical colourings in random graphs
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract Rödl and Ruciński (J. Amer. Math. Soc. 8 (1995), 917–942) established Ramsey's theorem for random graphs. In particular, for fixed integers r$r$, ℓ⩾2$\ell \geqslant 2$ they proved that p̂Kℓ,r(n)=n−2ℓ+1$\hat{p}_{K_\ell,r}(n)=n^{-\frac{2}{\ell +1}}$ is a threshold for the Ramsey property that every r$r$‐colouring of the edges of the binomial ...
Nina Kamčev, Mathias Schacht
wiley +1 more source
Journal of Quaternary Science, Volume 40, Issue 5, Page 778-793, July 2025.ABSTRACT Northwest Europe experienced high‐amplitude climate change at the onset and end of the Younger Dryas (YD; ca 12 800–11 600 cal a BP), a crucial period to develop our understanding of natural climate dynamics. European palaeoclimatological records generally suggest a bipartite structure of the YD, potentially due to a northward retreat of the ...
Christopher P. Francis +5 more
wiley +1 more source
Essentially tight bounds for rainbow cycles in proper edge‐colourings
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract An edge‐coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a variety of areas.
Noga Alon +4 more
wiley +1 more source
Journal of Systematics and Evolution, Volume 63, Issue 2, Page 319-330, March 2025.Using phylogenomics and allele frequency‐based approach based on multiple plastid and low‐copy nuclear genes, we confirm the hybrid origin of Dactylorhiza cantabrica, an endemic allopolyploid orchid from north‐western Iberia, as well as the clear genetic differentiation of the two parental species.
Eva Pardo Otero +3 more
wiley +1 more source
Combinatorial theorems relative to a random set [PDF]
, 2014 We describe recent advances in the study of random analogues of combinatorial theorems.Comment: 26 pages.
Conlon, David
core +2 more sources
Size‐Ramsey numbers of graphs with maximum degree three
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract The size‐Ramsey number r̂(H)$\hat{r}(H)$ of a graph H$H$ is the smallest number of edges a (host) graph G$G$ can have, such that for any red/blue colouring of G$G$, there is a monochromatic copy of H$H$ in G$G$. Recently, Conlon, Nenadov and Trujić showed that if H$H$ is a graph on n$n$ vertices and maximum degree three, then r̂(H)=O(n8/5 ...
Nemanja Draganić, Kalina Petrova
wiley +1 more source
Ramsey numbers for partially-ordered sets [PDF]
, 2016 We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets
Cox, Christopher, Stolee, Derrick
core