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Linear inequalities among graph invariants: UsingGraPHedronto uncover optimal relationships

Julie Christophe, Sophie Dewez, Jean-Paul Doignon, Gilles Fasbender, Philippe Grégoire, David Huygens, Martine Labbé, Sourour Elloumi, Hadrien Mélot, Hande Yaman
2008 Networks  
Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach.  ...  By definition, the optimal linear inequalities correspond to the facets of this polytope.  ...  R p valid for the polytope of graph invariants induces a linear relationship among the invariants under investigation, which holds for the class C.  ... 
doi:10.1002/net.20250 fatcat:ibzw6bntsfawpgtn57lrfxumdq

Connected vertex covers in dense graphs

Jean Cardinal, Eythan Levy
2010 Theoretical Computer Science  
We give new approximation results for this problem in dense graphs, in which either the minimum or the average degree is linear.  ...  The new algorithm approximates the minimum connected vertex cover problem within a factor strictly less than 2 on all dense graphs. All these results are shown to be tight.  ...  inequalities among graph invariants.  ... 
doi:10.1016/j.tcs.2010.03.021 fatcat:i22tudemw5c3xeie64hrh5ii74

Connected Vertex Covers in Dense Graphs [chapter]

Jean Cardinal, Eythan Levy
Lecture Notes in Computer Science  
We give new approximation results for this problem in dense graphs, in which either the minimum or the average degree is linear.  ...  The new algorithm approximates the minimum connected vertex cover problem within a factor strictly less than 2 on all dense graphs. All these results are shown to be tight.  ...  among graph invariants.  ... 
doi:10.1007/978-3-540-85363-3_4 fatcat:a7epabazvjfybilqijtqfdczlq