Dualizing Distance-Hereditary Graphs

Dualizing Distance-Hereditary Graphs

Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle/cutset duality as in abstract matroidal dualit...

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Bibliographic Details
Main Author: McKee Terry A.
Format: Article
Language:English
Published: Sciendo 2021-02-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
distance-hereditary graph
dual graph
graph duality
05c12
05c75
05c76
Online Access:https://doi.org/10.7151/dmgt.2192
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spelling doaj-689e4e0bd374402d9b62a800ec3b714f2021-09-05T17:20:24ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922021-02-0141128529610.7151/dmgt.2192dmgt.2192Dualizing Distance-Hereditary GraphsMcKee Terry A.0Department of Mathematics and Statistics, Wright State University, Dayton, Ohio45435USADistance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle/cutset duality as in abstract matroidal duality. The resulting “DH* graphs” are characterized and then analyzed in terms of connectivity. These results are used in a special case of plane-embedded graphs to justify viewing DH* graphs as the duals of distance-hereditary graphs.https://doi.org/10.7151/dmgt.2192distance-hereditary graphdual graphgraph duality05c1205c7505c76
collection DOAJ
language English
format Article
sources DOAJ
author McKee Terry A.
spellingShingle McKee Terry A.
Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae Graph Theory
distance-hereditary graph
dual graph
graph duality
05c12
05c75
05c76
author_facet McKee Terry A.
author_sort McKee Terry A.
title Dualizing Distance-Hereditary Graphs
title_short Dualizing Distance-Hereditary Graphs
title_full Dualizing Distance-Hereditary Graphs
title_fullStr Dualizing Distance-Hereditary Graphs
title_full_unstemmed Dualizing Distance-Hereditary Graphs
title_sort dualizing distance-hereditary graphs
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2021-02-01
description Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle/cutset duality as in abstract matroidal duality. The resulting “DH* graphs” are characterized and then analyzed in terms of connectivity. These results are used in a special case of plane-embedded graphs to justify viewing DH* graphs as the duals of distance-hereditary graphs.
topic distance-hereditary graph
dual graph
graph duality
05c12
05c75
05c76
url https://doi.org/10.7151/dmgt.2192
work_keys_str_mv AT mckeeterrya dualizingdistancehereditarygraphs
_version_ 1717786359818616832

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