Newly found forbidden graphs for trivializability

Ryo Nikkuni; Makoto Ozawa; Kouki Taniyama; Yukihiro Tsutsumi

doi:10.1142/S0218216505003932

Newly found forbidden graphs for trivializability

Ryo Nikkuni^*, Makoto Ozawa, Kouki Taniyama, Yukihiro Tsutsumi

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

Original language	English
Pages (from-to)	523-538
Number of pages	16
Journal	Journal of Knot Theory and its Ramifications
Volume	14
Issue number	4
DOIs	https://doi.org/10.1142/S0218216505003932
Publication status	Published - 2005 Jun

Keywords

Knotted projection
Spatial graph
Trivializable graph

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216505003932

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title = "Newly found forbidden graphs for trivializability",

abstract = "A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.",

keywords = "Knotted projection, Spatial graph, Trivializable graph",

author = "Ryo Nikkuni and Makoto Ozawa and Kouki Taniyama and Yukihiro Tsutsumi",

note = "Funding Information: The first and last authors were supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.",

year = "2005",

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T1 - Newly found forbidden graphs for trivializability

AU - Nikkuni, Ryo

AU - Ozawa, Makoto

AU - Taniyama, Kouki

AU - Tsutsumi, Yukihiro

N1 - Funding Information: The first and last authors were supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

PY - 2005/6

Y1 - 2005/6

N2 - A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

AB - A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

KW - Knotted projection

KW - Spatial graph

KW - Trivializable graph

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 4

ER -

Newly found forbidden graphs for trivializability

Abstract

Keywords

ASJC Scopus subject areas

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