𝔖 Bobbio Scriptorium
✦   LIBER   ✦

OnKs-free subgraphs inKs+k-free graphs and vertex Folkman numbers

✍ Scribed by Andrzej Dudek; Vojtěch Rödl


Publisher
Springer-Verlag
Year
2011
Tongue
English
Weight
248 KB
Volume
31
Category
Article
ISSN
0209-9683

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


Subgraphs in vertex neighborhoods of Kr-
✍ Jorgen Bang-Jensen; Stephan Brandt 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 111 KB

## Abstract In a __K~r~__‐free graph, the neighborhood of every vertex induces a __K__~__r__ − 1~‐free subgraph. The __K~r~__‐free graphs with the converse property that every induced __K__~__r__ − 1~‐free subgraph is contained in the neighborhood of a vertex are characterized, based on the charact

Long Cycles and 3-Connected Spanning Sub
✍ B. Jackson; N.C. Wormald 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 238 KB

Let \(G\) be a 3-connected \(K_{1, d}\)-free graph on \(n\) vertices. We show that \(G\) contains a 3-connected spanning subgraph of maximum degree at most \(2 d-1\). Using an earlier result of ours, we deduce that \(G\) contains a cycle of length at least \(\frac{1}{2} n^{c}\) where \(c=\left(\log

K4-free graphs with no odd hole: Even pa
✍ Yori Zwols 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB

An odd hole in a graph is an induced cycle of odd length at least five. In this article we show that every imperfect K 4 -free graph with no odd hole either is one of two basic graphs, or has an even pair or a clique cutset. We use this result to show that every K 4 -free graph with no odd hole has

Minimum independent generalized t-degree
✍ O. Favaron; Y. Redouane 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 448 KB

The minimum independent generalized t-degree of a graph G = (V,E) is ut = min{ IN(H H is an independent set of t vertices of G}, with N(H) = UxtH N(x). In a KI,~+I -free graph, we give an upper bound on u! in terms of r and the independence number CI of G. This generalizes already known results on u