Document Zbl 0768.90075

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II: Clique-web inequalities.</strong> <i>(English)</i> <a class="label nowrap" href="/0768.90075">Zbl 0768.90075</a> </h2> <div class="source"> <a href="/serials/1746" title="Journal Profile">Math. Program., Ser. A</a> <a href="/?q=in%3A9833" title="Articles in this Issue">56, No. 2, 161-188 (1992)</a>. </div> <div class="abstract">Summary: [For part I see the authors, ibid. 56A, No. 2, 121-160 (1992; <a href="/0768.90074">Zbl 0768.90074</a>).]<br class="zbmathjax-paragraph">We study new classes of facets for the cut cone $C_ n$ generated by the cuts of the complete graph on $n$ vertices. This cone can also be interpreted as the cone of all semi-metrics on $n$ points that are isometrically $l_ 1$-embeddable and, in fact, the study of the facets of the cut polytope is in some sense equivalent to the study of the facets of $C_ n$. These new facets belong to the class of clique-web inequalities which generalize the hypermetric and cycle inequalities as well as the bicycle odd wheel inequalities.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A94844">Cited in <strong>3</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A94844">Cited in <strong>22</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C35" title="MSC2020">90C35</a> </td> <td class="space"> Programming involving graphs or networks </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A52B12" title="MSC2020">52B12</a> </td> <td class="space"> Special polytopes (linear programming, centrally symmetric, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C27" title="MSC2020">90C27</a> </td> <td class="space"> Combinatorial optimization </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aantiweb">antiweb</a>; <a href="/?q=ut%3Ahypermetric+inequality">hypermetric inequality</a>; <a href="/?q=ut%3Afacets+for+the+cut+cone">facets for the cut cone</a>; <a href="/?q=ut%3Asemi-metrics">semi-metrics</a>; <a href="/?q=ut%3Aclique-web+inequalities">clique-web inequalities</a>; <a href="/?q=ut%3Acycle+inequalities">cycle inequalities</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0768.90074">Zbl 0768.90074</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0768.90075" data-ciurl="/ci/00094844" data-biburl="/bibtex/00094844.bib" data-amsurl="/amsrefs/00094844.bib" data-xmlurl="/xml/00094844.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00094844.pdf" title="Zbl 0768.90075 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF01580898" aria-label="DOI for “Facets for the cut cone. II: Clique-web inequalities”" title="10.1007/BF01580898">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://basepub.dauphine.fr/handle/123456789/14448" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">N. Alon, ”The CW-inequalities for vectors inl 1,”European Journal of Combinatorics 11 (1990) 1–6. · <a href="/0742.05077" class="nowrap">Zbl 0742.05077</a></td> </tr><tr> <td>[2]</td> <td class="space">P. Assouad and M. Deza, ”Espaces métriques plongeables dans un hypercube: aspects combinatoires,”Annals of Discrete Mathematics 8 (1980) 197–210. · <a href="/0464.05029" class="nowrap">Zbl 0464.05029</a> · <a href="https://doi.org/10.1016/S0167-5060(08)70874-4" class="nowrap">doi:10.1016/S0167-5060(08)70874-4</a></td> </tr><tr> <td>[3]</td> <td class="space">P. Assouad and M. Deza, ”Metric subspaces ofL 1,”Publications mathématiques d’Orsay 3 (1982). · <a href="/0478.05021" class="nowrap">Zbl 0478.05021</a></td> </tr><tr> <td>[4]</td> <td class="space">D. Avis and M. Deza, ”The cut cone,L 1-embeddability, complexity and multicommodity flows,”Networks 21 (1991) 595–617. · <a href="/0748.90015" class="nowrap">Zbl 0748.90015</a> · <a href="https://doi.org/10.1002/net.3230210602" class="nowrap">doi:10.1002/net.3230210602</a></td> </tr><tr> <td>[5]</td> <td class="space">F. Barahona, M. Grötschel, M. Jünger and G. Reinelt, ”An application of combinatorial optimization to statistical physics and circuit layout design,”Operations Research 36(3) (1988) 493–513. · <a href="/0646.90084" class="nowrap">Zbl 0646.90084</a> · <a href="https://doi.org/10.1287/opre.36.3.493" class="nowrap">doi:10.1287/opre.36.3.493</a></td> </tr><tr> <td>[6]</td> <td class="space">F. Barahona, M. Grötschel and A.R. Mahjoub, ”Facets of the bipartite subgraph polytope,”Mathematics of Operations Research 10 (1985) 340–358. · <a href="/0578.05056" class="nowrap">Zbl 0578.05056</a> · <a href="https://doi.org/10.1287/moor.10.2.340" class="nowrap">doi:10.1287/moor.10.2.340</a></td> </tr><tr> <td>[7]</td> <td class="space">F. Barahona and A.R. Mahjoub, ”On the cut polytope,”Mathematical Programming 36 (1986) 157–173. · <a href="/0616.90058" class="nowrap">Zbl 0616.90058</a> · <a href="https://doi.org/10.1007/BF02592023" class="nowrap">doi:10.1007/BF02592023</a></td> </tr><tr> <td>[8]</td> <td class="space">M. Conforti, M.R. Rao and A. Sassano, ”The equipartition polytope I,II,”Mathematical Programming 49 (1990) 49–70, 71–91. · <a href="/0718.90092" class="nowrap">Zbl 0718.90092</a> · <a href="https://doi.org/10.1007/BF01588778" class="nowrap">doi:10.1007/BF01588778</a></td> </tr><tr> <td>[9]</td> <td class="space">C. De Simone, M. Deza and M. Laurent, ”Collapsing and lifting for the cut cone,” to appear in:Proceedings of the Second Japan Conference on Graph Theory and Combinatorics (Hakone, 1990). · <a href="/0799.90099" class="nowrap">Zbl 0799.90099</a></td> </tr><tr> <td>[10]</td> <td class="space">M. Deza, ”On the Hamming geometry of unitary cubes,”Doklady Adademii Nauk SSR 134 (1960) 1037–1040. [English translation in:Soviet Physics Doklady 5 (1961) 940–943.]</td> </tr><tr> <td>[11]</td> <td class="space">M. Deza, ”Matrices de formes quadratiques non négatives pour des arguments binaires,”Comptes Rendus de l’Académie des Sciences de Paris 277 (1973) 873–875. · <a href="/0275.05014" class="nowrap">Zbl 0275.05014</a></td> </tr><tr> <td>[12]</td> <td class="space">M. Deza, K. Fukuda and M. Laurent, ”The inequicut cone,” Research Report No. 89-04, GSSM, University of Tsukuba (Tokyo, 1989). · <a href="/0801.52006" class="nowrap">Zbl 0801.52006</a></td> </tr><tr> <td>[13]</td> <td class="space">M. Deza, V.P. Grishukhin and M. Laurent, ”The symmetries of the cut polytope and of some relatives,” P. Gritzmann and B. Sturmfels, eds.,Applied Geometry and Discrete Mathematics, The ”Victor Klee Festschrift”, DIMACS series in Discrete Mathematics and Theoretical Computer Sciences 4 (1991) 205–220. · <a href="/0748.05061" class="nowrap">Zbl 0748.05061</a></td> </tr><tr> <td>[14]</td> <td class="space">M. Deza, V.P. Grishukhin and M. Laurent, ”The hypermetric cone is polyhedral,” to appear in:Combinatorica. · <a href="/0801.52009" class="nowrap">Zbl 0801.52009</a></td> </tr><tr> <td>[15]</td> <td class="space">M. Deza, M. Grötschel and M. Laurent, ”Clique-web facets for multicut polytopes,” to appear in:Mathematics of Operations Research. · <a href="/0762.90079" class="nowrap">Zbl 0762.90079</a></td> </tr><tr> <td>[16]</td> <td class="space">M. Deza and M. Laurent, ”Facets for the cut cone I,”Mathematical Programming 56 (1992) 121–160, this issue. · <a href="/0768.90074" class="nowrap">Zbl 0768.90074</a> · <a href="https://doi.org/10.1007/BF01580897" class="nowrap">doi:10.1007/BF01580897</a></td> </tr><tr> <td>[17]</td> <td class="space">M. Deza and M. Laurent, ”New results on facets of the cut cone,” to appear in:R.C. Bose Memorial Issue, Journal of Combinatorics, Information and System Sciences (1992). · <a href="/1230.05173" class="nowrap">Zbl 1230.05173</a></td> </tr><tr> <td>[18]</td> <td class="space">J.B. Kelly, ”Hypermetric spaces,”Lectures Notes in Mathematics No. 490 (Springer, Berlin, 1975) pp. 17–31. · <a href="/0325.52021" class="nowrap">Zbl 0325.52021</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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