TY - JOUR

T1 - On minimally 3-connected graphs on a surface

AU - Ota, Katsuhiro

PY - 2002/7/1

Y1 - 2002/7/1

N2 - It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

AB - It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

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U2 - 10.1016/S1571-0653(05)80006-X

DO - 10.1016/S1571-0653(05)80006-X

M3 - Article

AN - SCOPUS:34247107687

VL - 11

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -