Abstract
Cycle completable graphs were originally defined to answer matrix completion problems and have since received diverse graph-theoretic descriptions, in spite of not directly mentioning cycles. This paper characterizes such graphs by their chordless cycles never having ``bridges'' (as defined in H.-J. Voss's 1991 monograph {\em Cycles and Bridges in Graphs\/}) that have more than two vertices of attachment in the cycle. This approach is then related to the well-studied, yet seemingly quite distinct, classes of chordal graphs and series-parallel graphs. This is done by allowing chords to be ``bridges'' that have exactly two vertices of attachment.
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Recommended Citation
McKee, Terry A.
(2026)
"Cycle-Based Characterizations of the Cycle Completable Graphs,"
Theory & Applications of Graphs: Vol. 12:
Iss.
2, Article 6.
DOI: 10.20429/tag.2025.120206
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol12/iss2/6
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