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9.501  Articles
1 of 951 pages  |  10  records  |  more records»
Let G and H be two given graphs. The notation F?(G,H) means that any red-blue coloring on the edges of F will create either a red subgraph G or a blue subgraph H in F. A graph F is a Ramsey (G,H)-minimal graph if F satisfies two conditions: (1) F?(G,H), a... see more

Let F, G and H be any simple graphs. The notation F ? (G, H) means for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. If F ? (G, H), then graph... see more

Let F, G and H be simple graphs. The notation F ? (G, H) means that for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. A graph F is called... see more

In 2005, Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow, immediately leading to an explicit representation of this invariant in many concrete cases. More recently, ... see more

For fixed finite graphs GG, HH, a common problem in Ramsey theory is to study graphs FF such that F?(G,H)F \to (G,H), i.e. every red-blue coloring of the edges of FF produces either a red GG or a blue HH. We generalize this study to infinite graphs GG, HH... see more

This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers.  We offer several general theorems, some of which focus on Ramsey-good cases (i.e., case... see more

A graph class is said to be tame if graphs in the class have a polynomially bounded number of minimal separators. Tame graph classes have good algorithmic properties, which follow, for example, from an algorithmic metatheorem of Fomin, Todinca, and Villan... see more

A proper edge coloring of a class 2 graph G is minimal if it contains a color class of cardinality equal to the resistance r(G) of G, which is the minimum number of edges that have to be removed from G to obtain a graph which is ?(G)-edge colorable, ... see more

Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, r(G,H), is the minimum size of F. If the order of F ... see more

1 of 951 pages  |  10  records  |  more records»