Geodesic
Strongly Unichord-Free Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 365-374

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

Several recent papers have investigated unichord-free graphs—the graphs in which no cycle has a unique chord. This paper proposes a concept of strongly unichord-free graph, defined by being unichord-free with no cycle of length 5 or more having exactly two chords. In spite of its overly simplistic look, this can be regarded as a natural strengthening of unichordfree graphs—not just the next step in a sequence of strengthenings—and it has a variety of characterizations. For instance, a 2-connected graph is strongly unichord-free if and only if it is complete bipartite or complete or “minimally 2-connected” (defined as being 2-connected such that deleting arbitrary edges always leaves non-2-connected subgraphs).
Keywords: unichord-free graph, strongly chordal graph 
@article{DMGT_2019_39_2_a5,
     author = {McKee, Terry A.},
     title = {Strongly {Unichord-Free} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {365--374},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a5/}
}
TY  - JOUR
AU  - McKee, Terry A.
TI  - Strongly Unichord-Free Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2019
SP  - 365
EP  - 374
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a5/
LA  - en
ID  - DMGT_2019_39_2_a5
ER  - 
%0 Journal Article
%A McKee, Terry A.
%T Strongly Unichord-Free Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2019
%P 365-374
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a5/
%G en
%F DMGT_2019_39_2_a5
McKee, Terry A. Strongly Unichord-Free Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 365-374. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a5/