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## Filters

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Linear inequalities among graph invariants: UsingGraPHedronto uncover optimal relationships

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. ...

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Connected vertex covers in dense graphs

2010
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Theoretical Computer Science
*

We give new approximation results for this problem in dense

doi:10.1016/j.tcs.2010.03.021
fatcat:i22tudemw5c3xeie64hrh5ii74
*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*. ...##
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Connected Vertex Covers in Dense Graphs
[chapter]

*
Lecture Notes in Computer Science
*

We give new approximation results for this problem in dense

doi:10.1007/978-3-540-85363-3_4
fatcat:a7epabazvjfybilqijtqfdczlq
*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*. ...