scholarly journals Edge-ordered Ramsey numbers

2020 ◽  
Vol 87 ◽  
pp. 103100
Author(s):  
Martin Balko ◽  
Máté Vizer
Keyword(s):  
Ramsey Numbers

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

scholarly journals A Note on On-Line Ramsey Numbers for Some Paths

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 735
Author(s):  
Tomasz Dzido ◽  
Renata Zakrzewska
Keyword(s):  
Ramsey Number ◽  
Ramsey Numbers ◽  
Minimum Number ◽  
On Line ◽  
Infinite Set ◽  
Do So

We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11.

A Note on On-Line Ramsey Numbers of Stars and Paths

2021 ◽  
Author(s):  
Fatin Nur Nadia Binti Mohd Latip ◽  
Ta Sheng Tan
Keyword(s):  
Ramsey Numbers ◽  
On Line

Bipartite Ramsey numbers of Kt,s in many colors

2021 ◽  
Vol 404 ◽  
pp. 126220
Author(s):  
Ye Wang ◽  
Yusheng Li ◽  
Yan Li
Keyword(s):  
Ramsey Numbers

scholarly journals Turán theorems for unavoidable patterns

2021 ◽  
pp. 1-20
Author(s):  
ANTÓNIO GIRÃO ◽  
BHARGAV NARAYANAN
Keyword(s):  
Complete Graph ◽  
Blow Up ◽  
Ramsey Numbers ◽  
Order Of Magnitude ◽  
Transitive Tournament ◽  
Unavoidable Patterns

Abstract We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and by Fox and Sudakov. First, for t ≥ 3, we show that any two-colouring of the complete graph on n vertices that is δ-far from being monochromatic contains an unavoidable t-colouring when δ ≫ n−1/t, where an unavoidable t-colouring is any two-colouring of a clique of order 2t in which one colour forms either a clique of order t or two disjoint cliques of order t. Next, for t ≥ 3, we show that any tournament on n vertices that is δ-far from being transitive contains an unavoidable t-tournament when δ ≫ n−1/[t/2], where an unavoidable t-tournament is the blow-up of a cyclic triangle obtained by replacing each vertex of the triangle by a transitive tournament of order t. Conditional on a well-known conjecture about bipartite Turán numbers, both our results are sharp up to implied constants and hence determine the order of magnitude of the corresponding off-diagonal Ramsey numbers.

scholarly journals Small order graph-tree Ramsey numbers

1988 ◽  
Vol 72 (1-3) ◽  
pp. 119-127 ◽  
Author(s):  
R.J. Faudree ◽  
C.C. Rousseau ◽  
R.H. Schelp
Keyword(s):  
Ramsey Numbers ◽  
Graph Tree

scholarly journals Configurations in projective planes and quadrilateral-star Ramsey numbers

2008 ◽  
Vol 308 (17) ◽  
pp. 3986-3991 ◽  
Author(s):  
E.L. Monte Carmelo
Keyword(s):  
Projective Planes ◽  
Ramsey Numbers

Ramsey Numbers Involving Graphs with Long Suspended Paths

1981 ◽  
Vol s2-24 (3) ◽  
pp. 405-413 ◽  
Author(s):  
S. A. Burr
Keyword(s):  
Ramsey Numbers

scholarly journals Ramsey Numbers for Theta Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
M. M. M. Jaradat ◽  
M. S. A. Bataineh ◽  
S. M. E. Radaideh
Keyword(s):  
Complete Graph ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Subgraph Isomorphic

The graph Ramsey number is the smallest integer with the property that any complete graph of at least vertices whose edges are colored with two colors (say, red and blue) contains either a subgraph isomorphic to all of whose edges are red or a subgraph isomorphic to all of whose edges are blue. In this paper, we consider the Ramsey numbers for theta graphs. We determine , for . More specifically, we establish that for . Furthermore, we determine for . In fact, we establish that if is even, if is odd.

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