This paper aims to give a brief introduction to a set of problems, old and new, concerned with one of the main and long-standing quests in infinite graph theory: how to represent the end structure of a given graph by that of a simpler subgraph, in particular a spanning tree. There has been a fair am
On the Ramsey multiplicities of graphs—problems and recent results
✍ Scribed by Stefan A. Burr; Vera Rosta
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 610 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Ramsey's theorem guarantees that if G is a graph, then any 2‐coloring of the edges of a large enough complete graph yields a monochromatic copy of G. Interesting problems arise when one asks how many such G must occur. A survey of this and related problems is given, along with a number of new results.
📜 SIMILAR VOLUMES
## Abstract We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr et al. We determine the corresponding graph parameter for numerous bipartite graphs, including bi‐regular bipartite graphs and forests. We also make initial progress for graphs of l
The aim of this paper is to show the existence of metrics gÄ = on S n , where gÄ = is a perturbation of the standard metric gÄ 0 , for which the Yamabe problem possesses a sequence of solutions unbounded in L (S n ). The metrics gÄ = that we find are of class C k on S n with (k n&3 4 ). We also prov
Let x(G) and o(G) denote the chromatic number and clique number of a graph G. We prove that x can be bounded by a function of o for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line
Let G be a graph and let t Ն 0 be a real number. Then, We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sufficient degree conditions implying that (G) Ն t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.