K  6 ‐minors in triangulations and complete quadrangulations | Zendy

Mukae Raiji | Zendy; Nakamoto Atsuhiro | Zendy

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K 6 ‐minors in triangulations and complete quadrangulations

Author(s) -

Mukae Raiji,

Nakamoto Atsuhiro

Publication year - 2009

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20360

Subject(s) - mathematics , combinatorics , conjecture , triangulation , projective plane , planar , graph , toroid , planar graph , discrete mathematics , geometry , computer science , physics , computer graphics (images) , quantum mechanics , correlation , plasma

In this paper, we shall prove that a projective‐planar (resp., toroidal) triangulation G has K 6 as a minor if and only if G has no quadrangulation isomorphic to K 4 (resp., K 5 ) as a subgraph. As an application of the theorems, we can prove that Hadwiger's conjecture is true for projective‐planar and toroidal triangulations. © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 302‐312, 2009

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