Results 1 to 10 of about 52 (52)
Star-Critical Ramsey Numbers for Cycles Versus K4
Discussiones Mathematicae Graph Theory, 2021 Given three graphs G, H and K we write K → (G, H), if in any red/blue coloring of the edges of K there exists a red copy of G or a blue copy of H. The Ramsey number r(G, H) is defined as the smallest natural number n such that Kn → (G, H) and the star ...
Jayawardene Chula J. +2 more
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Gallai-Ramsey Numbers for Rainbow S3+S_3^ + and Monochromatic Paths
Discussiones Mathematicae Graph Theory, 2022 Motivated by Ramsey theory and other rainbow-coloring-related problems, we consider edge-colorings of complete graphs without rainbow copy of some fixed subgraphs.
Li Xihe, Wang Ligong
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Ramsey numbers of cycles versus general graphs
Forum of Mathematics, Sigma, 2023 The Ramsey number $R(F,H)$ is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that, for any graph H, provided n is sufficiently large, a ...
John Haslegrave +3 more
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Tower Gaps in Multicolour Ramsey Numbers
Forum of Mathematics, Sigma, 2023 Resolving a problem of Conlon, Fox and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their $2$ -colour and q-colour Ramsey numbers.
Quentin Dubroff +3 more
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On Small Balanceable, Strongly-Balanceable and Omnitonal Graphs
Discussiones Mathematicae Graph Theory, 2022 In Ramsey Theory for graphs we are given a graph G and we are required to find the least n0 such that, for any n ≥ n0, any red/blue colouring of the edges of Kn gives a subgraph G all of whose edges are blue or all are red.
Caro Yair, Lauri Josef, Zarb Christina
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Edge-maximal -free non-bipartite Hamiltonian graphs of odd order
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] denote the class of non-bipartite graphs on n vertices containing no [Formula: see text]-graph and [Formula: see text] Let [Formula: see text] denote the class of non-bipartite Hamiltonian graphs on n vertices containing no ...
M. M. M. Jaradat +4 more
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Avoiding rainbow 2-connected subgraphs
Open Mathematics, 2017 While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to ...
Gorgol Izolda
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Antipodal Edge-Colorings of Hypercubes
Discussiones Mathematicae Graph Theory, 2019 Two vertices of the k-dimensional hypercube Qkare antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y.
West Douglas B., Wise Jennifer I.
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On the Restricted Size Ramsey Number Involving a Path P3
Discussiones Mathematicae Graph Theory, 2019 For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey number r*(G,H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G,H), and bounded below by e(G) + e(H) − 1 ...
Silaban Denny Riama +2 more
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Proof of a conjecture of Galvin
Forum of Mathematics, Pi, 2020 We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours.
Dilip Raghavan, Stevo Todorcevic
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