The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear.
The gap of the graph of a matrix
โ Scribed by Javad Faghih-Habibi
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 116 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _
The nonsingular submatrices of maximum order of the complete and the reduced incidence matrices over the real jield of a graph are shown to be in one-to-one correspondence with the odd generalized circuits and the odd generalized k-trees of the graph, respectively. It is also shown that the positiv