Binding number, minimum degree and (g,f)-factors of graphs
DOI:
https://doi.org/10.11575/cdm.v13i2.62686Keywords:
Graph TheoryAbstract
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.
References
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3. R. Diestel, Graph theory, 4th ed., Graduate Texts in Mathematics, vol. 173, Springer, 2010.
4. M. Kano and N. Tokushige, Binding numbers and f-factors of graphs, J. Combin. Theory Ser. B 54 (1992), 213-221.
5. L. Lovász, Subgraphs with prescribed valencies, J. Combin. Theory 8 (1970), 391-416.
6. N. Tokushige, Binding number and minimum degree for k-factors, J. Graph Theory 13 (1989), 607-617.
7. D. R. Woodall, The binding number of a graph and its Anderson number, J. Combin. Theory Ser. B 15 (1973), 225-255.
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