Lovász theta-function of graphs¶
AUTHORS:
- Dima Pasechnik (2015-06-30): Initial version 
REFERENCE:
Functions¶
- sage.graphs.lovasz_theta.lovasz_theta(graph)[source]¶
- Return the value of Lovász theta-function 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 setset of \(G\) and the- chromatic numberof the- complement\(\overline{G}\) of \(G\).- For more information, see the Wikipedia article Lovász_number. - Note - Implemented for undirected graphs only. Use - to_undirectedto convert a digraph to an undirected graph.
- This function requires the optional package - csdp, which you can install with- sage -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 - >>> from sage.all import * >>> C = graphs.PetersenGraph() >>> C.lovasz_theta() # optional - csdp 4.0 >>> graphs.CycleGraph(Integer(5)).lovasz_theta() # optional - csdp 2.236068