𝔖 Bobbio Scriptorium
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An Improvement of the Godsil Bound

✍ Scribed by Akira Hiraki; Jack Koolen


Book ID
105764613
Publisher
Springer
Year
2002
Tongue
English
Weight
106 KB
Volume
6
Category
Article
ISSN
0218-0006

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## 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 ℝ^2^ plane. The conjecture made by ErdΕ‘s in 1973 that __cr__(__G__) β‰₯ __Cm__^3^/__n__^2^ was proved in 1982 by Leighton

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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.

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