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Large faces in 4-critical planar graphs with minimum degree 4 (1995)

Abbott, H. L. ; Hare, D. R. ; Zhou, B.

Springer

Combinatorica 15 (1995), S. 455-467

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ISSN: 1439-6912

Keywords: Primary 05C15 ; Secondary 05C35

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We prove that the size of the largest face of a 4-critical planar graph with δ≥4 is at most one half the number of its vertices. Letf(n) denote the maximum of the sizes of largest faces of all such graphs withn vertices (n sufficiently large). We present an infinite family of graphs that shows $$\mathop {\lim }\limits_{n \to \infty } \frac{{f(n)}}{n} = \frac{1}{2}$$ .

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01192518

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