Ramsey numbers
Size Multipartite Ramsey Numbers for Small Paths vs. K_{2,n}
... classical Ramsey numbers have been studied for a few decades (see Radziszowski, 2017 for a survey) but sadly not much progress has been done even in the case of ...classical Ramsey numbers and ...
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Star-Critical Ramsey Numbers for Cycles Versus the Complete Graph on 5 Vertices
... the Ramsey numbers r(n, m) defined r(n, m) = r(Kn, ...classical Ramsey number, introduced by Hook and Isaak in 2010 (see [6]), is the Star-critical Ramsey ...-critical Ramsey number is ...
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Some Multicolor Ramsey Numbers Involving Cycles
... It is not known whether or not there exists a polynomial-time algo- rithm to test whether two graphs are isomorphic or not [GJ79]. On the other hand, it is easy to see that this problem is crucial for graph theory ...
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A Study on Ramsey Numbers and its Bounds
... In real life Ramsey numbers are used .As noted by Slany, combinatorial games “serve as models that simplify the analysis of competitive situations as models that simplify the analysis of competitive ...
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Calculating Ramsey numbers by partitioning colored graphs
... on Ramsey numbers of graphs [6], the exact value of the Ramsey number R(G, H ) is only known when G and H each belong to one of a few families of ...
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A General Lower Bound on Gallai-Ramsey Numbers for Non-Bipartite Graphs
... Given a graph H with a pair of nonadjacent vertices u and v, let H uv be the reduction of H obtained from H by identifying u and v to a single vertex (removing any multiple copies of edges that were created in the ...
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Applying a genetic algorithm to improve the lower bounds of multi-color ramsey numbers
... Rochester Institute of Technology Department of Computer Science Applying a Genetic Algorithm to Improve the Lower Bounds of Multi-Color Ramsey Numbers Shardul Rao A thesis, submitted to[r] ...
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Zarankiewicz Numbers and Bipartite Ramsey Numbers
... In this work, we design and exploit a computational method for bounding and computing Zarankiewicz num- bers. Using it, we obtain several new values and bounds on z(b; s) for 3 ≤ s ≤ 6. Our approach and new knowl- edge ...
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THE SIZE MULTIPARTITE RAMSEY NUMBERS $m_j(P_n,K_{j\times b})$
... balanced multipartite graphs, the numbers can be derived from result Burger and van Vuuren [1]. Gy´ arf´ as et al. [2] studied the Ramsey-type problem in directed and bipartite graphs. Furthermore, ...
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Size Multipartite Ramsey Numbers for K4-e Versus all Graphs up to 4 Vertices
... diagonal Ramsey number of r ( s s , ) (see [6] for a survey) has not made any headway beyond r (5,5) (as of now known to be between 43 and 49) for a few ...classical Ramsey numbers, introduced by ...
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Bipartite Ramsey Numbers and Zarankiewicz Numbers
... ble, and his value was only off by one. This discrepancy is significant because at least one author (H´ eger) has reported the erroneous value as well as further values based on it without having checked Guy’s tables ...
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Size Multipartite Ramsey Numbers for Small Paths Versus Stripes
... If we were left with two vertices by the third remark we can increase the blue matching size by 1 as the two remaining vertices must be connected by a blue edge and obta[r] ...
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Ramsey numbers involving a triangle: theory and algorithms
... What There are other related results obtained only triangle not corresponding graphs Ramsey vertices containing one It is easy to graphs It is G on 7 for n relations 7 = very interesting[r] ...
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Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
... number of edges in a graph G such that any proper edge-coloring of G contains a rainbow copy of H. The size anti-Ramsey number was originally defined in [20] along with several notions of online anti-Ramsey ...
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Ramsey goodness of paths
... It is a corollary of the celebrated theorem of Ramsey that these numbers are always finite. Let χ(H) be the chromatic number of H, i.e. the smallest number of colors needed to color the vertices of H so ...
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An Application of the Ramsey Number in the Electricity Pricing
... of Ramsey number was first proposed by the British mathematician Ramsey in ...the Ramsey number, but now the exact value of the Ramsey number having been developed by people remains ...into ...
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On a Ramsey Problem Involving the 3-Pan Graph
... M.Christou, S.Iliopoulos and M.Miller, Bipartite Ramsey numbers involving stars, stripes and trees, Electronic Journal of Graph Theory and Applications, 1(2) (2013) 89-99. S.Sy[r] ...
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Singular Ramsey and Turán numbers
... consider Ramsey-type results for two colors, and develop a couple of methods suitable for determining the exact value of singular Ramsey numbers in both the diagonal and non-diagonal cases, provided ...
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$m_j(P_4,G)$ for all Graphs G on 4 Vertices
... A.P.Burger and J.H.van Vuuren, Ramsey numbers in complete balanced multipartite graphs. V.Chavatal and F.Harary, Generalized Ramsey theory for graphs, III.[r] ...
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A Size Multipartite Ramsey Problem Involving the Claw Graph
... Syafrizal Sy and E.T.Baskoro, Lower bounds of the size multipartite Ramsey numbers, The 5 th Mathematics, AIP Conf.[r] ...
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