On a conjecture of bondy
โ Scribed by I Fournier; P Fraisse
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 412 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Our aim in this note is to prove a conjecture of Bondy, extending a classical theorem of Dirac to edge-weighted digraphs: if every vertex has out-weight at least 1 then the digraph contains a path of weight at least 1. We also give several related conjectures and results concerning heavy cycles in e
Let f # Z[x] with degree k and let p be a prime. By a complete trigonometric sum we mean a sum of the form S(q, f )= q x=1 e q ( f (x)), where q is a positive integer and e q (:)=exp(2?if (x)รq). Professor Chalk made a conjecture on the upper bound of S(q, f ) when q is a prime power. We prove Chalk
Dirac proved in 1952 that every 2-connected graph of order n and minimum degree k admits a cycle of length at least minfn; 2kg: As a possible improvement, Woodall conjectured in 1975 that if a 2-connected graph of order n has at least n 2 รพ k vertices of degree at least k; then it has a cycle of len