Contractions of 6-connected toroidal graphs

Authors:
Gašper Fijavž
Affiliations:
Institute for Mathematics, Physics, and Mechanics, Jadranska 19, Ljubljana, Slovenia and Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, Ljubljana, Slov ...
Venue:
Journal of Combinatorial Theory Series B
Year:
2007

Citing 3
Cited 1

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Abstract

Let T"6 denote the class of all 6-connected (equivalently 6-regular) toroidal graphs and let G@?T"6 which is not minor-minimal in T"6. Let G^'@?T"6 be a proper minor of G with maximum number of vertices. We show that |V(G)|-|V(G^')|=fw(G), where fw(G) denotes the face-width of the toroidal embedding of G. Consequently, we show that the only minor-minimal graphs in T"6 are K"7, K"8-4K"2, K"9-C"9, and K"9-3K"3.