Let X Ο Ν 1 , 2 , . . . , n Ν be a set of n elements and let X ( r ) be the collection of all the subsets of X containing precisely r elements . Then the generalised Kneser graph K ( n , r , s ) (when 2 r Οͺ s Ρ n ) is the graph with vertex set X ( r ) and edges AB for A , B X ( r ) with Ν A Κ B Ν Ρ
Explicit 2-Factorisations of the Odd Graph
β Scribed by J. Robert Johnson; H. A. Kierstead
- Book ID
- 106489538
- Publisher
- Springer Netherlands
- Year
- 2004
- Tongue
- English
- Weight
- 93 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N
In this note, we settle a problem of N. Biggs [4, p. 801 by showing that for each k, no distance regular graph non-isomorphic to the odd graph Ok can have the same parameters as Ok. A related charxterization of certain graphs associated with the Johnson scheme J(2& + 1, k) is also g&en. By a graph w