Hypergraphs with no special cycles
β Scribed by Richard Anstee
- Book ID
- 110564334
- Publisher
- Springer-Verlag
- Year
- 1983
- Tongue
- English
- Weight
- 342 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We give constructions of colorβcritical graphs and hypergraphs with no short cycles and with relatively few edges. In particular, we show that, for each __n__ β§ 3, the smallest number of edges in a 3βcritical triangleβfree __n__βgraph (hypergraph) with __m__ vertices is __m__ + __o(m)__
We give constructions of color-critical graphs and hypergraphs with no cycles of length 5 or shorter and with relatively few edges.
To a graph G is canonically associated its neighborhood-hypergraph, X(G), formed by the closed neighborhoods of the vertices of G. We characterize the graphs G such that (i) X(G) has no induced cycle, or (ii) #(G) is a balanced hypergraph or (iii) X(G) is triangle free. (i) is another short proof of
Soit H = (X. ~1 un hypergraphe h-uniforme avec IX] = net soit L h ~(H! le graphe Jont les sommets reprdsentent les arates de H, deux sommets 6lant reli6s si et seulement si t~s z~r6tes qu'ils reprdsen!ent intersectent en h -1 sommet,=. Nous montrons que sif,, t(H) ne contienl pas de cycle, alors I~[