𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a conjecture of bollobás and bosák

✍ Scribed by Štefan Znám

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
364 KB
Volume
6
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

It is shown that, for all sufficiently large k, the complete graph K~n~ can be decomposed into k factors of diameter 2 if and only if n ≥ 6__k__.

📜 SIMILAR VOLUMES

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) .

Proof of a Conjecture of Bollob?s on Nes
Proof of a Conjecture of Bollob?s on Nested Cycles
✍ Guantao Chen; Paul Erdós; William Staton 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 221 KB

For any positive integer k, a minimum degree condition is obtained which forces a graph to have k edge-disjoint cycles C 1 , C 2 , ..., C k such that V(C 1

On a Conjecture of Kátai for Additive Fu
On a Conjecture of Kátai for Additive Functions
✍ Eduard Wirsing; Tang Yuan-sheng; Shao Pin-tsung 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 181 KB

Ka tai himself gave partial solutions. In he proved that &2f (n)&=0(n &1 ) ( 3 ) article no. 0027

On a Conjecture of Nicolas–Sárközy about
On a Conjecture of Nicolas–Sárközy about Partitions
✍ F. Ben saı̈d 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 152 KB

Let N be the set of positive integers, B ¼ fb 1 5 . . . 5b k g & N, N 2 N, and N5b k . For i ¼ 0 or 1, A ¼ A i ðB; NÞ is the set (introduced by Nicolas, Ruzsa, and Sa´rko¨zy, J. Number Theory 73 (1998), 292-317) such that A \ f1; . . . ; Ng ¼ B and pðA; nÞ iðmod2Þ for n 2 N; n4N, where pðA; nÞ denot

Proof of a Conjecture of Mader, Erdös an
Proof of a Conjecture of Mader, Erdös and Hajnal on Topological Complete Subgraphs
✍ B. Bollobás; A. Thomason 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 89 KB

We show that every graph G of size at least 256 p 2 |G| contains a topological complete subgraph of order p. This slight improvement of a recent result of Komlós and Szemerédi proves a conjecture made by Mader and by Erdös and Hajnal.

On a Conjecture of Lovász Concerning Bri
On a Conjecture of Lovász Concerning Bricks: II. Bricks of Finite Characteristic
✍ Marcelo H. de Carvalho; Cláudio L. Lucchesi; U.S.R. Murty 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 271 KB

we established the validity of the main theorem (1.1) for solid bricks. Here, we establish the existence of suitable separating cuts in nonsolid bricks and prove the theorem by applying induction to cut-contractions with respect to such cuts.