It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k ≥ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n ≥ 3k, i.e., M (k) ≤ 3k. W
Proof of a Conjecture of Bollob?s on Nested Cycles
✍ Scribed by Guantao Chen; Paul Erdós; William Staton
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 221 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
✦ Synopsis
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
📜 SIMILAR VOLUMES
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) .
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C. Reutenauer (Adv. in Math. 110 (1995), 234 246) has defined a new class of symmetric functions q \* indexed by partitions \*. He conjectures that for n 2, &q (n) is the sum of Schur symmetric functions. This paper provides a proof of his conjecture.