A result on fractional k-deleted graphs

• Autores: Sizhong Zhou
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 106, Nº 1, 2010, págs. 99-106
• Idioma: inglés
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• Resumen

  • Let k≥2 be an integer, and let G be a graph of order n with n≥4k−5. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. The binding number of G is defined as 26741 {\operatorname {bind}} (G)=\min\left\{\frac{|N_G(X)|}{|X|}:\emptyset\neq X\subseteq V(G),N_G(X)\neq V(G)\right\}. 26741 In this paper, it is proved that if bind(G)>(2k−1)(n−1)k(n−2), then G is a fractional k-deleted graph. Furthermore, it is shown that the result in this paper is best possible in some sense.