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The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

✍ Scribed by Yusheng Li; Wenan Zang


Book ID
111592073
Publisher
Springer US
Year
2003
Tongue
English
Weight
110 KB
Volume
7
Category
Article
ISSN
1382-6905

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πŸ“œ SIMILAR VOLUMES


Independence numbers of locally sparse g
✍ Noga Alon πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 409 KB πŸ‘ 1 views

Let G = (V, E ) be a graph on n vertices with average degree t 2 1 in which for every vertex u E V the induced subgraph on the set of all neighbors of u is r-colorable. We show that the independence number of G is at least log t , for some absolute positive constant c. This strengthens a well-known

Ramsey Numbers and the Size of Graphs
✍ Sudakov, Benny πŸ“‚ Article πŸ“… 2008 πŸ› Society for Industrial and Applied Mathematics 🌐 English βš– 151 KB
On the Ramsey number of trees versus gra
✍ Ronald J. Gould; Michael S. Jacobson πŸ“‚ Article πŸ“… 1983 πŸ› John Wiley and Sons 🌐 English βš– 335 KB

Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3

On the Maximum Number of Independent Cyc
✍ Hong Wang πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 404 KB

Let G=(V 1 , V 2 ; E ) be a bipartite graph with |V 1 |= |V 2 | =n 2k, where k is a positive integer. Suppose that the minimum degree of G is at least k+1. We show that if n>2k, then G contains k vertex-disjoint cycles. We also show that if n=2k, then G contains k&1 quadrilaterals and a path of orde