Fractional Clique Number
المؤلف:
Godsil, C. and Royle, G.
المصدر:
Fractional Clique Number." §7.2 in Algebraic Graph Theory. New York: Springer-Verlag
الجزء والصفحة:
...
4-3-2022
2098
Fractional Clique Number
The maximum possible weight of a fractional clique of a graph 
is called the fractional clique number of 
, denoted 
(Godsil and Royle 2001, pp. 136-137) or 
(Larson et al. 1995). Every simple graph has a fractional clique number which is a rational number or integer.
The fractional clique number satisfies
where 
is the clique number, 
is the fractional chromatic number, and 
is the chromatic number (Godsil and Royle 2001, pp. 141 and 145), where the result 
follows from the strong duality theorem for linear programming (Larson et al. 1995; Godsil and Royle 2001, p. 141).
REFERENCES
Godsil, C. and Royle, G. "Fractional Clique Number." §7.2 in Algebraic Graph Theory. New York: Springer-Verlag, pp. 136-137, 2001.
Larsen, M.; Propp, J.; and Ullman, D. "The Fractional Chromatic Number of Mycielski's Graphs." J. Graph Th. 19, 411-416, 1995.
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