Central European Journal of Mathematics

, Volume 6, Issue 4, pp 543–558 | Cite as

Disjoint triangles and quadrilaterals in a graph

  • Hong WangEmail author
Research Article


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.


cover cycle factor 


05C38 05C70 


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  1. [1]
    Bollobás B., Extremal graph theory, Academic Press, London-New York, 1978zbMATHGoogle Scholar
  2. [2]
    Corrádi K., Hajnal A., On the maximal number of independent circuits in a graph, Acta Math. Acad. Sci. Hungar., 1963, 14, 423–439zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    El-Zahar M.H., On circuits in graphs, Discrete Math., 1984, 50, 227–230CrossRefMathSciNetGoogle Scholar
  4. [4]
    Enomoto H., On the existence of disjoint cycles in a graph, Combinatorica, 1998, 18, 487–492zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Erdős P., Some recent combinatroial problems, Technical Report, University of Bielefeld, November 1990Google Scholar
  6. [6]
    Randerath B., Schiermeyer I., Wang H., On quadrilaterals in a graph, Discrete Math., 1999, 203, 229–237.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Wang H., On the maximum number of independent cycles in a graph, Discrete Math., 1990, 205, 183–190CrossRefGoogle Scholar
  8. [8]
    Wang H., Vertex-disjoint quadrilaterals in graphs, Discrete Math., 2004, 288, 149–166zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Wnag H., Proof of the Erdős-Faudree Conjecture on Quadrilaterals, preprintGoogle Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Department of MathematicsThe University of IdahoMoscowUSA

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