COUNTING LINKS IN COMPLETE GRAPHS

被引：0

作者：

Fleming, Thomas ^{[1
]}

Mellor, Blake ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Loyola Marymount Univ, Dept Math, Los Angeles, CA 90045 USA

来源：

OSAKA JOURNAL OF MATHEMATICS | 2009年 / 46卷 / 01期

关键词：

COMPLETE BIPARTITE GRAPHS; SPATIAL GRAPHS; PAGENUMBER; KNOTS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the minimal number of non-trivial links in an embedding of any complete k-partite graph on 7 vertices (including K(7). which has at least 21 non-trivial links). We give either exact values or upper and lower bounds for the minimal number of non-trivial links for all complete k-partite graphs on 8 vertices. We also look at larger complete bipartite graphs. and state a conjecture relating minimal linking embeddings with minimal book embeddings.

引用

页码：173 / 201

页数：29

共 15 条

[1]

[Anonymous], 1971, RECENT TRENDS GRAPH, DOI DOI 10.1007/BFB0059432

[2] BOOK THICKNESS OF A GRAPH [J].

BERNHART, F ;

KAINEN, PC .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1979, 27 (03) :320-331

[3] KNOTS AND LINKS IN SPATIAL GRAPHS [J].

CONWAY, JH ;

GORDON, CM .

JOURNAL OF GRAPH THEORY, 1983, 7 (04) :445-453

[4] On the pagenumber of complete bipartite graphs [J].

Enomoto, H ;

Nakamigawa, T ;

Ota, K .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1997, 71 (01) :111-120

[5] Intrisically n-linked graphs [J].

Flapan, E ;

Pommersheim, J ;

Foisy, J ;

Naimi, R .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2001, 10 (08) :1143-1154

[6]

FLAPAN E, FUND MATH IN PRESS

[7]

Flapan Erica, 2002, ALGEBR GEOM TOPOL, V2, P371

[8] Intrinsic linking and knotting in virtual spatial graphs [J].

Fleming, Thomas ;

Mellor, Blake .

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2007, 7 :583-601

[9] Intrinsically linked graphs and even linking number [J].

Fleming, Thomas ;

Diesl, Alexander .

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2005, 5 :1419-1432

[10] On the size of links in Kn,n, Kn,n,1, and Kn [J].

Johnson, B ;

Johnson, W .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2002, 11 (02) :145-151

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