Abstract
Let H be a set of connected graphs, each of which has order at least three, and suppose that there exist infinitely many connected H-free graphs of minimum degree at least two and all except for finitely many of them have a 2-factor. In [J. Graph Theory, 64 (2010), 250–266], we proved that if |H| ≤ 3, then one of the members in H is a star. In this article, we determine the remaining members of H and hence give a complete characterization of the pairs and triples of forbidden subgraphs.
| Original language | English |
|---|---|
| Pages (from-to) | 61-82 |
| Number of pages | 22 |
| Journal | Journal of Graph Theory |
| Volume | 90 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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Keywords
- 2-factor
- forbidden subgraph
ASJC Scopus subject areas
- Geometry and Topology
Cite this
Pairs and triples of forbidden subgraphs and the existence of a 2-factor. / Aldred, R. E.L.; Fujisawa, Jun; Saito, Akira.
In: Journal of Graph Theory, Vol. 90, No. 1, 01.01.2019, p. 61-82.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Pairs and triples of forbidden subgraphs and the existence of a 2-factor
AU - Aldred, R. E.L.
AU - Fujisawa, Jun
AU - Saito, Akira
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Let H be a set of connected graphs, each of which has order at least three, and suppose that there exist infinitely many connected H-free graphs of minimum degree at least two and all except for finitely many of them have a 2-factor. In [J. Graph Theory, 64 (2010), 250–266], we proved that if |H| ≤ 3, then one of the members in H is a star. In this article, we determine the remaining members of H and hence give a complete characterization of the pairs and triples of forbidden subgraphs.
AB - Let H be a set of connected graphs, each of which has order at least three, and suppose that there exist infinitely many connected H-free graphs of minimum degree at least two and all except for finitely many of them have a 2-factor. In [J. Graph Theory, 64 (2010), 250–266], we proved that if |H| ≤ 3, then one of the members in H is a star. In this article, we determine the remaining members of H and hence give a complete characterization of the pairs and triples of forbidden subgraphs.
KW - 2-factor
KW - forbidden subgraph
UR - http://www.scopus.com/inward/record.url?scp=85056425436&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85056425436&partnerID=8YFLogxK
U2 - 10.1002/jgt.22368
DO - 10.1002/jgt.22368
M3 - Article
VL - 90
SP - 61
EP - 82
JO - Journal of Graph Theory
JF - Journal of Graph Theory
SN - 0364-9024
IS - 1
ER -