Results 71 to 80 of about 248,095 (281)
R ( 5 , 5 ) ≤ 46 $R(5,5)\le 46$
Journal of Graph Theory, EarlyView.ABSTRACT We prove that the Ramsey number R ( 5 , 5 ) $R(5,5)$ is less than or equal to 46. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computational parts of the proof were independently implemented by both authors, with consistent results.
Vigleik Angeltveit, Brendan D. McKay
wiley +1 more source
Anti-Ramsey numbers of small graphs [PDF]
, 2013 The anti-Ramsey number $AR(n,G$), for a graph $G$ and an integer $n\geq|V(G)|$, is defined to be the minimal integer $r$ such that in any edge-colouring of $K_n$ by at least $r$ colours there is a multicoloured copy of $G$, namely, a copy of $G$ whose ...
Bialostocki, Arie +2 more
core
Treewidth Versus Clique Number. V. Further Connections With Tree‐Independence Number
Journal of Graph Theory, EarlyView.ABSTRACT We continue the study of ( tw , ω ) $({\mathsf{tw}},\omega )$‐bounded graph classes, that is, hereditary graph classes in which large treewidth is witnessed by the presence of a large clique, and the relation of this property to boundedness of the tree‐independence number, a graph parameter introduced independently by Yolov in 2018 and by ...
Claire Hilaire +2 more
wiley +1 more source
The k-Ramsey number of two five cycles
AKCE International Journal of Graphs and CombinatoricsGiven any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all ...
Johannes H. Hattingh +2 more
doaj +1 more source
Ramsey numbers of Berge-hypergraphs and related structures [PDF]
, 2019 For a graph $G=(V,E)$, a hypergraph $\mathcal{H}$ is called a Berge-$G$, denoted by $BG$, if there exists a bijection $f: E(G) \to E(\mathcal{H})$ such that for every $e \in E(G)$, $e \subseteq f(e)$.
Salia, Nika +3 more
core +1 more source
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
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
On Monochromatic Subgraphs of Edge-Colored Complete Graphs
Discussiones Mathematicae Graph Theory, 2014 In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic.
Andrews Eric +4 more
doaj +1 more source
Journal of Combinatorial Theory, Series B, 1974 AbstractLet f(m,n) be the least integer N such that for every graph G with N vertices, either G contains a path of m vertices or the complement of G contains a vertex of degree at least n. This paper determines f(m,n) for all m, n.
openaire +2 more sources
A Guide to Key Decision Criteria for Likert‐Scale Use in Survey Research
Global Business and Organizational Excellence, EarlyView.ABSTRACT Although widely used in survey research, the application of the Likert scale often lacks rigorous justification in relation to key methodological decisions. Furthermore, inconsistencies in terminology persist, for example, the common reference made to the “5‐point Likert scale,” even though debate is ongoing about the optimal number of ...
Khan Md Raziuddin Taufique +2 more
wiley +1 more source