Necessary and Sufficient Conditions for a Property on Graphs to be Characterizable in Terms of <I>k</I>-Connected (<I>k</I><cd02161.gif>1, 2, 3) Forbidden Graphs

Takao ASANO

Necessary and Sufficient Conditions for a Property on Graphs to be Characterizable in Terms of k-Connected (k1, 2, 3) Forbidden Graphs

Takao ASANO

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Some properties ^π on graphs are characterized in terms of a set S(π) of forbidden graphs, that is, a graph G satisfies property π if and only if G has no subgraph homeomorphic (subcontraction isomorphic) to graph in S(π). Among such properties, ^πplanarity" is the most famous, where S(π){K_{3, 3}, K₅}. This paper clarifies the relations among such properties and presents necessary and sufficient conditions for a property to be characterizable in terms of k-connected (k1, 2, 3) forbidden graphs.

Publication: IEICE TRANSACTIONS on transactions Vol.E66-E No.11 pp.666-670

Publication Date: 1983/11/25

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Type of Manuscript: PAPER

Category: Circuit Theory

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Takao ASANO

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Takao ASANO, "Necessary and Sufficient Conditions for a Property on Graphs to be Characterizable in Terms of k-Connected (k1, 2, 3) Forbidden Graphs" in IEICE TRANSACTIONS on transactions, vol. E66-E, no. 11, pp. 666-670, November 1983, doi: .
Abstract: Some properties ^π on graphs are characterized in terms of a set S(π) of forbidden graphs, that is, a graph G satisfies property π if and only if G has no subgraph homeomorphic (subcontraction isomorphic) to graph in S(π). Among such properties, ^πplanarity" is the most famous, where S(π){K_{3, 3}, K₅}. This paper clarifies the relations among such properties and presents necessary and sufficient conditions for a property to be characterizable in terms of k-connected (k1, 2, 3) forbidden graphs.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e66-e_11_666/_p

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@ARTICLE{e66-e_11_666,
author={Takao ASANO, },
journal={IEICE TRANSACTIONS on transactions},
title={Necessary and Sufficient Conditions for a Property on Graphs to be Characterizable in Terms of k-Connected (k1, 2, 3) Forbidden Graphs},
year={1983},
volume={E66-E},
number={11},
pages={666-670},
abstract={Some properties ^π on graphs are characterized in terms of a set S(π) of forbidden graphs, that is, a graph G satisfies property π if and only if G has no subgraph homeomorphic (subcontraction isomorphic) to graph in S(π). Among such properties, ^πplanarity" is the most famous, where S(π){K_{3, 3}, K₅}. This paper clarifies the relations among such properties and presents necessary and sufficient conditions for a property to be characterizable in terms of k-connected (k1, 2, 3) forbidden graphs.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Necessary and Sufficient Conditions for a Property on Graphs to be Characterizable in Terms of k-Connected (k1, 2, 3) Forbidden Graphs
T2 - IEICE TRANSACTIONS on transactions
SP - 666
EP - 670
AU - Takao ASANO
PY - 1983
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E66-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1983
AB - Some properties ^π on graphs are characterized in terms of a set S(π) of forbidden graphs, that is, a graph G satisfies property π if and only if G has no subgraph homeomorphic (subcontraction isomorphic) to graph in S(π). Among such properties, ^πplanarity" is the most famous, where S(π){K_{3, 3}, K₅}. This paper clarifies the relations among such properties and presents necessary and sufficient conditions for a property to be characterizable in terms of k-connected (k1, 2, 3) forbidden graphs.
ER -