Binding number, minimum degree and (g,f)-factors of graphs

Takamasa Yashima

Abstract


Let a and b be integers with 2<= a< b, and let G be a graph of order n with n>= (a+b-1)^2/(a+1) and the minimum degree \delta(G)<= 1+(((b-2)n)/(a+b-1)).
Let g and f be nonnegative integer-valued functions defined on V(G) such that a<= g(x)<f(x)<= b for each x in V(G).

We prove that if the binding number bind(G)>=1+((b-2)/(a+1)), then G has a (g,f)-factor.


Keywords


Graph Theory

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DOI: https://doi.org/10.11575/cdm.v13i2.62686

DOI (PDF): https://doi.org/10.11575/cdm.v13i2.62686.g46824

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Contributions to Discrete Mathematics. ISSN: 1715-0868