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Fractionally colouring total graphs. (English) Zbl 0795.05056
To any simple graph \(G=(V,E)\) with maximum vertex degree \(\Delta\) we form a total graph with stable set \(T\) on the vertex set \(V(G) \cup E(G)=F\). It is shown that a feasible solution of the minimum in the linear program \[ \min \left\{ w\bar 1:w \geq 0,\sum_{u \in T} w_ T \geq 1,\;u \in F,\;T \in {\mathcal S} \right\} \] is bounded above by \(\Delta+2\), where \({\mathcal S}\) is the family of total stable sets of \(G\).
Reviewer: J.Fiamcik

05C15 Coloring of graphs and hypergraphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
90C10 Integer programming
Full Text: DOI
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