The maximal size of the covering graph of a lattice
✍ Scribed by Béla Bollobás; Ivan Rival
- Book ID
- 112761251
- Publisher
- Springer
- Year
- 1979
- Tongue
- English
- Weight
- 100 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0002-5240
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## Abstract Let __G__ be a graph and let __k__′(__G__) be the edge‐connectivity of __G__. The __strength__ of __G__, denoted by k̄′(__G__), is the maximum value of __k__′(__H__), where __H__ runs over all subgraphs of __G__. A simple graph __G__ is called k‐__maximal__ if k̄′(__G__) ≤ __k__ but for
Jakubik has shown that for discrete modular lattices all graph isomorphisms are given by certain direct product decompositions. Duffus and Rival have proved a similar theorem for graded lattices which are atomistic and coatomistic. Modifying some of the results of Duffus and Rival we give a common g
Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch