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4-valent graphs

✍ Scribed by T. C. Enns

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 707 KB
Volume: 6
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190060303

No coin nor oath required. For personal study only.

✦ Synopsis

Let bk}k22, k+4 be a sequence of non-negative integers which satisfies 8 + &(k -4)pk = 0. Then there exists an integer p4 such that there exists a 2-connected planar graph with exactly pk k-gons as faces for all k 1 2 . This paper determines all such p4 when pk = 0 f o r k 1 5 and determines that there is a constant C 2 1 such that for some rn 5 pz +ap3 + C, there exists a 2connected planar graph with exactly pk faces for each p 4 = m + 2 w , w a positive integer. When there exists at least one odd k 1 3 for which pk # 0, the coefficient 2 of w in the above equation may be replaced by 1. These conclusions do not hold if the coefficients of p2 and p J are any smaller than 1 and i, respectively.

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