Geodesic
Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 285-296.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: distance-hereditary graph, dual graph, graph duality 
@article{DMGT_2021_41_1_a17,
     author = {McKee, Terry A.},
     title = {Dualizing {Distance-Hereditary} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {285--296},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a17/}
}
TY  - JOUR
AU  - McKee, Terry A.
TI  - Dualizing Distance-Hereditary Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2021
SP  - 285
EP  - 296
VL  - 41
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a17/
LA  - en
ID  - DMGT_2021_41_1_a17
ER  - 
%0 Journal Article
%A McKee, Terry A.
%T Dualizing Distance-Hereditary Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2021
%P 285-296
%V 41
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a17/
%G en
%F DMGT_2021_41_1_a17
McKee, Terry A. Dualizing Distance-Hereditary Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 285-296. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a17/

[1] D.W. Barnette, On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs, in: The Many Facets of Graph Theory, G. Chartrand and S.F. Kapoor (Ed(s)), Lecture Notes in Math. 110 (Springer, Berlin, 1969) 27–40. doi: 10.1007/BFb0060102

[2] H.-J. Bandelt and H.M. Mulder, Distance-hereditary graphs, J. Combin. Theory Ser. B 41 (1986) 182–208. doi: 10.1016/0095-8956(86)90043-2

[3] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia, 1999). doi: 10.1137/1.9780898719796

[4] E. Howorka, A characterization of distance-hereditary graphs, Q. J. Math. 28 (1977) 417–420. doi: 10.1093/qmath/28.4.417

[5] T.A. McKee, Dual properties within graph theory, Fund. Math. 128 (1987) 91–97. doi: 10.4064/fm-128-2-91-97

[6] T.A. McKee, Recognizing dual-chordal graphs, Congr. Numer. 150 (2001) 97–103.

[7] T.A. McKee, Dualizing chordal graphs, Discrete Math. 263 (2003) 207–219. doi: 10.1016/S0012-365X(02)00577-0

[8] K. Truemper, On Whitney’s 2-isomorphism theorem for graphs, J. Graph Theory 4 (1980) 43–49. doi: 10.1002/jgt.3190040106

[9] H. Whitney, 2-isomorphic graphs, Amer. J. Math. 55 (1933) 245–254. doi: 10.2307/2371127

[10] R. Wilson, Introduction to Graph Theory, Fourth Edition (Longman, Harlow, 1996).

[11] X. Yu, On the cycle-isomorphism of graphs, J. Graph Theory 15 (1991) 19–27. doi: 10.1002/jgt.3190150105