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The number of connected sparsely edged graphs. IV large nonseparable graphs

✍ Scribed by E. M. Wright

Publisher: John Wiley and Sons
Year: 1983
Tongue: English
Weight: 306 KB
Volume: 7
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190070211

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✦ Synopsis

The number of nonseparable graphs on n labeled points and q lines is u(n, 9). In the second paper of this series an exact formula for u(n, n + k) was found for general n and successive (small) k. The method would give an asymptotic approximation for fixed k as n + 30. Here an asymptotic approximation to u(n, n + k) is found when k = O(n'/') and an approximation to logu(n, n + k ) when k < (1 -E ) ( + n)1'2. The problem of finding an approximation to u(n, 9) when (qn)/nl/' -+ + 33 and q / n -4 logn -4 log logn +x is open.

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