Lovász thetafunction of graphs¶
AUTHORS:
 Dima Pasechnik (20150630): Initial version
REFERENCE:
[Lovasz1979]  László Lovász, “On the Shannon capacity of a graph”, IEEE Trans. Inf. Th. 25(1979), 17. 
Functions¶

sage.graphs.lovasz_theta.
lovasz_theta
(graph)¶ Return the value of Lovász thetafunction of graph
For a graph \(G\) this function is denoted by \(\theta(G)\), and it can be computed in polynomial time. Mathematically, its most important property is the following:
\[\alpha(G)\leq\theta(G)\leq\chi(\overline{G})\]with \(\alpha(G)\) and \(\chi(\overline{G})\) being, respectively, the maximum size of an
independent set
set of \(G\) and thechromatic number
of thecomplement
\(\overline{G}\) of \(G\).For more information, see the Wikipedia article Lovász_number.
Note
 Implemented for undirected graphs only. Use
to_undirected
to convert a digraph to an undirected graph.  This function requires the optional package
csdp
, which you can install withsage i csdp
.
EXAMPLES:
sage: C = graphs.PetersenGraph() sage: C.lovasz_theta() # optional csdp 4.0 sage: graphs.CycleGraph(5).lovasz_theta() # optional csdp 2.236068
 Implemented for undirected graphs only. Use