Results 31 to 40 of about 4,692 (164)
Local colourings and monochromatic partitions in complete bipartite graphs
, 2016 We show that for any $2$-local colouring of the edges of the balanced complete bipartite graph $K_{n,n}$, its vertices can be covered with at most~$3$ disjoint monochromatic paths.
Lang, Richard, Stein, Maya
core +1 more source
Star-path and star-stripe bipartite Ramsey numbers in multicoloring [PDF]
Transactions on Combinatorics, 2015 For given bipartite graphs G 1 ,G 2 ,…,G t , the bipartite Ramsey number bR(G 1 ,G 2 ,…,G t ) is the smallest integer n such that if the edges of the complete bipartite graph K n,n are partitioned into t disjoint color classes giving t ...
Ghaffar Raeisi
doaj
The Bipartite $K_{2,2}$-Free Process and Bipartite Ramsey Number $b(2, t)$ [PDF]
The Electronic Journal of Combinatorics, 2020 The bipartite Ramsey number $b(s,t)$ is the smallest integer $n$ such that every blue-red edge coloring of $K_{n,n}$ contains either a blue $K_{s,s}$ or a red $K_{t,t}$. In the bipartite $K_{2,2}$-free process, we begin with an empty graph on vertex set $X\cup Y$, $|X|=|Y|=n$.
Bal, Deepak, Bennett, Patrick
openaire +3 more sources
Almost-Rainbow Edge-Colorings of Some Small Subgraphs
Discussiones Mathematicae Graph Theory, 2013 Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás.
Krop Elliot, Krop Irina
doaj +1 more source
On two problems in graph Ramsey theory [PDF]
, 2010 We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices.
A. Thomason +36 more
core +5 more sources
Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, EarlyView.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
wiley +1 more source
Ramsey numbers of ordered graphs
, 2019 An ordered graph is a pair $\mathcal{G}=(G,\prec)$ where $G$ is a graph and $\prec$ is a total ordering of its vertices. The ordered Ramsey number $\overline{R}(\mathcal{G})$ is the minimum number $N$ such that every ordered complete graph with $N ...
Balko, Martin +3 more
core +1 more source
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source
, 2009 Consider the following game between two players, Builder and Painter. Builder draws edges one at a time and Painter colours them, in either red or blue, as each appears.
Conlon, David
core +1 more source
Size‐Ramsey Numbers of Structurally Sparse Graphs
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT Size‐Ramsey numbers are a central notion in combinatorics and have been widely studied since their introduction by Erdős, Faudree, Rousseau, and Schelp in 1978. Research has mainly focused on the size‐Ramsey numbers of n$$ n $$‐vertex graphs with constant maximum degree Δ$$ \Delta $$.
Nemanja Draganić +4 more
wiley +1 more source