MacLane's planarity criterion for locally finite graphs

被引：25

作者：

Bruhn, H ^{[1
]}

Stein, M ^{[1
]}

机构：

[1] Univ Hamburg, Math Seminar, D-20146 Hamburg, Germany

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2006年 / 96卷 / 02期

关键词：

infinite graphs; planarity; cycle space;

D O I：

10.1016/j.jctb.2005.07.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B. Solving a problem of Wagner [Graphentheorie, Bibliographisches Institut, Mannheim, 1970], we show that the topological cycle space introduced recently by Diestel and Kuhn allows a verbatim generalisation of MacLane's criterion to locally finite graphs. This then enables us to extend Kelmans' planarity criterion as well. (C) 2005 Elsevier Inc. All rights reserved.

引用

页码：225 / 239

页数：15

共 15 条

[1]

Bondy J.A., 2008, GRAD TEXTS MATH

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