Finite contractions of graphs with polynomial growth

被引：5

作者：

Lukács, A

Seifter, N

机构：

[1] CWI, NL-1090 GB Amsterdam, Netherlands

[2] Montanuniv Leoben, Inst Math & Angew Geometrie, A-8700 Leoben, Austria

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2001年 / 22卷 / 01期

基金：

奥地利科学基金会;

关键词：

D O I：

10.1006/eujc.2000.0405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a locally finite, vertex-transitive, infinite graph with polynomial growth. Then there exists a quotient group of Aut(X) which contains a finitely generated nilpotent subgroup N which has the same growth rate as X. We show that X contains a subgraph which is finitely contractible onto the h-dimensional lattice, where h is the Hirsch number of N. (C) 2001 Academic Press.

引用

页码：85 / 90

页数：6

共 14 条

[1]

Babai Laszlo, 1977, J GRAPH THEOR, V1, P125

[2]

BASS H, 1972, P LOND MATH SOC, V25, P603

[3] A NOTE ON BOUNDED AUTOMORPHISMS OF INFINITE-GRAPHS [J].

GODSIL, CD ;

IMRICH, W ;

SEIFTER, N ;

WATKINS, ME ;

WOESS, W .

GRAPHS AND COMBINATORICS, 1989, 5 (04) :333-338

[4]

GROMOV M, 1981, PUBL MATH-PARIS, V53, P53

[5]

Halin R., 1973, Abh. Math. Sem. Univer. Hamburg, V39, P251, DOI [10.1007/BF02992834, DOI 10.1007/BF02992834]

[6] A SURVEY ON GRAPHS WITH POLYNOMIAL-GROWTH [J].

IMRICH, W ;

SEIFTER, N .

DISCRETE MATHEMATICS, 1991, 95 (1-3) :101-117

[7]

JUNG HA, 1984, EUROP J COMB, V5, P149

[8] Lattices in graphs with polynomial growth [J].

Lukacs, A ;

Seifter, N .

DISCRETE MATHEMATICS, 1998, 186 (1-3) :227-236

[9]

Segal D., 1983, POLYCYCLIC GROUPS

[10] Automorphism groups of graphs with quadratic growth [J].

Seifter, N ;

Trofimov, VI .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1997, 71 (02) :205-210

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