# Disjoint triangles and quadrilaterals in a graph

Open Mathematics (2008)

• Volume: 6, Issue: 4, page 543-558
• ISSN: 2391-5455

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## Abstract

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Let n, s and t be three integers with s ≥ 1, t ≥ 0 and n = 3s + 4t. Let G be a graph of order n such that the minimum degree of G is at least (n + s)/2. Then G contains a 2-factor with s + t components such that s of them are triangles and t of them are quadrilaterals.

## How to cite

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Hong Wang. "Disjoint triangles and quadrilaterals in a graph." Open Mathematics 6.4 (2008): 543-558. <http://eudml.org/doc/269292>.

@article{HongWang2008,
abstract = {Let n, s and t be three integers with s ≥ 1, t ≥ 0 and n = 3s + 4t. Let G be a graph of order n such that the minimum degree of G is at least (n + s)/2. Then G contains a 2-factor with s + t components such that s of them are triangles and t of them are quadrilaterals.},
author = {Hong Wang},
journal = {Open Mathematics},
keywords = {cover; cycle; factor},
language = {eng},
number = {4},
pages = {543-558},
title = {Disjoint triangles and quadrilaterals in a graph},
url = {http://eudml.org/doc/269292},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Hong Wang
TI - Disjoint triangles and quadrilaterals in a graph
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 543
EP - 558
AB - Let n, s and t be three integers with s ≥ 1, t ≥ 0 and n = 3s + 4t. Let G be a graph of order n such that the minimum degree of G is at least (n + s)/2. Then G contains a 2-factor with s + t components such that s of them are triangles and t of them are quadrilaterals.
LA - eng
KW - cover; cycle; factor
UR - http://eudml.org/doc/269292
ER -

## References

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1. [1] Bollobás B., Extremal graph theory, Academic Press, London-New York, 1978 Zbl0419.05031
2. [2] Corrádi K., Hajnal A., On the maximal number of independent circuits in a graph, Acta Math. Acad. Sci. Hungar., 1963, 14, 423–439 http://dx.doi.org/10.1007/BF01895727 Zbl0118.19001
3. [3] El-Zahar M.H., On circuits in graphs, Discrete Math., 1984, 50, 227–230 http://dx.doi.org/10.1016/0012-365X(84)90050-5
4. [4] Enomoto H., On the existence of disjoint cycles in a graph, Combinatorica, 1998, 18, 487–492 http://dx.doi.org/10.1007/s004930050034 Zbl0924.05041
5. [5] Erdős P., Some recent combinatroial problems, Technical Report, University of Bielefeld, November 1990
6. [6] Randerath B., Schiermeyer I., Wang H., On quadrilaterals in a graph, Discrete Math., 1999, 203, 229–237. http://dx.doi.org/10.1016/S0012-365X(99)00053-9 Zbl0932.05046
7. [7] Wang H., On the maximum number of independent cycles in a graph, Discrete Math., 1990, 205, 183–190 http://dx.doi.org/10.1016/S0012-365X(99)00009-6 Zbl0936.05063
8. [8] Wang H., Vertex-disjoint quadrilaterals in graphs, Discrete Math., 2004, 288, 149–166 http://dx.doi.org/10.1016/j.disc.2004.02.020 Zbl1102.05051
9. [9] Wnag H., Proof of the Erdős-Faudree Conjecture on Quadrilaterals, preprint Zbl1223.05145

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