Abstract
Let G be a simple graph and f an odd integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional (1, f)-odd factor if d F (v) ∈ {1, 3, ⋯ , f(v)} for all v ∈ V(G), where d F (v) is the fractional degree of v in F. In this paper, we discuss the existence for a graph to have a fractional (1,f)-odd-factor. A necessary and sufficient condition for a tree to have a fractional (1,f)-odd factor is given.
The work is supported by NNSF (10471078) of China and RFDP (20040422004), Promotional Foundation (2005BS01016) for Middle-aged or Young Scientists of Shandong Province, DRF and UF(XJ0609)of QFNU.
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Yu, J., Liu, G. (2007). Notes on Fractional (1,f)-Odd Factors of Graphs. In: Preparata, F.P., Fang, Q. (eds) Frontiers in Algorithmics. FAW 2007. Lecture Notes in Computer Science, vol 4613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73814-5_30
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DOI: https://doi.org/10.1007/978-3-540-73814-5_30
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