𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Erdős-Sós Conjecture for trees of diameter four

✍ Scribed by Andrew McLennan

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
100 KB
Volume
49
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The Erdős‐Sós Conjecture is that a finite graph G with average degree greater than k − 2 contains every tree with k vertices. Theorem 1 is a special case: every k‐vertex tree of diameter four can be embedded in G. A more technical result, Theorem 2, is obtained by extending the main ideas in the proof of Theorem 1. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 291–301, 2005

📜 SIMILAR VOLUMES

A Proof of a Partition Conjecture of Bat
A Proof of a Partition Conjecture of Bateman and Erdős
✍ Jason P Bell 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 97 KB

Bateman and Erdo s found necessary and sufficient conditions on a set A for the kth differences of the partitions of n with parts in A, p (k) A (n), to eventually be positive; moreover, they showed that when these conditions occur p (k+1) A (n) tends to zero as n tends to infinity. Bateman and Erdo

Proof of a Conjecture of Bollobás and Ko
Proof of a Conjecture of Bollobás and Kohayakawa on the Erdős–Stone Theorem
✍ Yoshiyasu Ishigami 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 242 KB

For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .

On an anti-Ramsey problem of Burr, Erdős
On an anti-Ramsey problem of Burr, Erdős, Graham, and T. Sós
✍ Gábor N. Sárközy; Stanley Selkow 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB

## Abstract Given a graph __L__, in this article we investigate the anti‐Ramsey number χ~__S__~(n,e,L), defined to be the minimum number of colors needed to edge‐color some graph __G__(__n__,__e__) with __n__ vertices and __e__ edges so that in every copy of __L__ in __G__ all edges have different