Improvement of the Greenberg-low bound
β Scribed by A. Martin
- Book ID
- 110652658
- Publisher
- Springer-Verlag
- Year
- 1966
- Weight
- 234 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0369-3546
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π SIMILAR VOLUMES
## Abstract The crossing number __cr__(__G__) of a simple graph __G__ with __n__ vertices and __m__ edges is the minimum number of edge crossings over all drawings of __G__ on the β^2^ plane. The conjecture made by ErdΕs in 1973 that __cr__(__G__)ββ₯β__Cm__^3^/__n__^2^ was proved in 1982 by Leighton
We show that the number of columns \(\left(c_{i}, a_{i}, b_{i}\right)=(1,1, k-2)\) in the intersection arrays of distance-regular graphs is at most three if the column \((1,0, k-1)\) exists. This improves the Bosheir-Nomura bound from four to three. 1994 Academic Press, Inc.