Some Results on Fractional Graph Theory

We will convert integer-based definitions and invariants into their fractional analogues. Some results on fractional factors, fractional Hamiltonian graphs, fractional (g ,f )-factors and fractional colorings are presented. The relationships of the programming and the graph theory are discussed. In particular, some new results related to fractional (g ,f )-factors obtained by us are given. Furthermore, some open problems are presented.

[1]  Ma Ying-hon.  Some Results on Fractional k-extendable Graphs , 2004 .

[2]  G Liu,et al.  ISOLATED TOUGHNESS AND THE EXISTENCE OF FRACTIONAL FACTORS , 2003 .

[3]  Yang Jing,et al.  FRACTIONAL(g,f)-FACTORS IN GRAPHS , 2001 .

[4]  László Lovász,et al.  Subgraphs with prescribed valencies , 1970 .

[5]  Dwight Duffus,et al.  Lexicographic matchings cannot form Hamiltonian cycles , 1988 .

[6]  Blow up behavior for a semilinear parabolic equation with localized source , 2009 .

[7]  W. T. Tutte.  The Factors of Graphs , 1952, Canadian Journal of Mathematics.

[8]  G. Tinhofer.  Graphen und Matrizen , 1976 .

[9]  YU Ji-gou.  Binding number and minimum degree conditions for graphs to have fractional factors , 2004 .

[10]  G. Liu,et al.  PROPERTIES OF FRACTIONAL K-FACTORS OF GRAPHS , 2005 .

[11]  C. Berge.  Fractional Graph Theory , 1978 .

[12]  Yan Liu,et al.  The fractional matching numbers of graphs , 2002, Networks.

[13]  David G. Kirkpatrick,et al.  A simple existence criterion for (g , 1990, Discret. Math..

[14]  William R. Pulleyblank.  Fractional matchings and the Edmonds-Gallai theorem , 1987, Discret. Appl. Math..

[15]  Richard P. Anstee,et al.  An Algorithmic Proof of Tutte's f-Factor Theorem , 1985, J. Algorithms.

[16]  L. Lovász.  Matching Theory (North-Holland mathematics studies) , 1986 .

[17]  Liu Guizhen.  Fractional k-Factors of Graphs , 2005 .

[18]  Jin Akiyama,et al.  Factors and factorizations of graphs - a survey , 1985, J. Graph Theory.

[19]  G. Liu,et al.  Fractional (g, f)-factors of graphs , 2001 .

[20]  E. Balas.  Integer and Fractional Matchings , 1981 .