<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00988176</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-26T02:46:24+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Long cycles in hypercubes with distant faulty vertices</title>
            <author role="aut">
              <persName>
                <forename type="first">Petr</forename>
                <surname>Gregor</surname>
              </persName>
              <idno type="halauthorid">825275-0</idno>
              <affiliation ref="#struct-251844"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Riste</forename>
                <surname>Škrekovski</surname>
              </persName>
              <idno type="halauthorid">467268-0</idno>
              <affiliation ref="#struct-119123"/>
              <affiliation ref="#struct-38374"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Service Ist</forename>
                <surname>Inria Sophia Antipolis-Méditerranée / I3s</surname>
              </persName>
              <email type="md5">7c88c2dda46d455591481b4e07aef779</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2014-05-07 16:03:56</date>
              <date type="whenModified">2026-03-12 08:32:02</date>
              <date type="whenReleased">2014-05-07 16:05:01</date>
              <date type="whenProduced">2009-01-01</date>
              <date type="whenEndEmbargoed">2014-05-07</date>
              <ref type="file" target="https://inria.hal.science/hal-00988176v1/document">
                <date notBefore="2014-05-07"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-00988176v1/file/1005-4198-3-PB.pdf" id="file-988176-750827">
                <date notBefore="2014-05-07"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="129574">
                <persName>
                  <forename>Service Ist</forename>
                  <surname>Inria Sophia Antipolis-Méditerranée / I3s</surname>
                </persName>
                <email type="md5">7c88c2dda46d455591481b4e07aef779</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00988176</idno>
            <idno type="halUri">https://inria.hal.science/hal-00988176</idno>
            <idno type="halBibtex">gregor:hal-00988176</idno>
            <idno type="halRefHtml">&lt;i&gt;Discrete Mathematics and Theoretical Computer Science&lt;/i&gt;, 2009, Vol. 11 no. 1 (1), pp.185--198. &lt;a target="_blank" href="https://dx.doi.org/10.46298/dmtcs.466"&gt;&amp;#x27E8;10.46298/dmtcs.466&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Discrete Mathematics and Theoretical Computer Science, 2009, Vol. 11 no. 1 (1), pp.185--198. &amp;#x27E8;10.46298/dmtcs.466&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-988176-750827"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="DMTCS">DMTCS</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">Graphs and Algorithms</note>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Long cycles in hypercubes with distant faulty vertices</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Petr</forename>
                    <surname>Gregor</surname>
                  </persName>
                  <idno type="halauthorid">825275-0</idno>
                  <affiliation ref="#struct-251844"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Riste</forename>
                    <surname>Škrekovski</surname>
                  </persName>
                  <idno type="halauthorid">467268-0</idno>
                  <affiliation ref="#struct-119123"/>
                  <affiliation ref="#struct-38374"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">649</idno>
                <idno type="issn">1462-7264</idno>
                <idno type="eissn">1365-8050</idno>
                <title level="j">Discrete Mathematics and Theoretical Computer Science</title>
                <imprint>
                  <publisher>DMTCS</publisher>
                  <biblScope unit="volume">Vol. 11 no. 1</biblScope>
                  <biblScope unit="issue">1</biblScope>
                  <biblScope unit="pp">185--198</biblScope>
                  <date type="datePub">2009-01-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.46298/dmtcs.466</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, we study long cycles in induced subgraphs of hypercubes obtained by removing a given set of faulty vertices such that every two faults are distant. First, we show that every induced subgraph of Q(n) with minimum degree n - 1 contains a cycle of length at least 2(n) - 2(f) where f is the number of removed vertices. This length is the best possible when all removed vertices are from the same bipartite class of Q(n). Next, we prove that every induced subgraph of Q(n) obtained by removing vertices of some given set M of edges of Q(n) contains a Hamiltonian cycle if every two edges of M are at distance at least 3. The last result shows that the shell of every linear code with odd minimum distance at least 3 contains a Hamiltonian cycle. In all these results we obtain significantly more tolerable faulty vertices than in the previously known results. We also conjecture that every induced subgraph of Q(n) obtained by removing a balanced set of vertices with minimum distance at least 3 contains a Hamiltonian cycle.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-251844" status="VALID">
          <orgName>Department of Theoretical Computer Science and Mathematical Logic [Prague]</orgName>
          <desc>
            <address>
              <addrLine>Charles University in Prague Faculty of Mathematics and Physics Malostranské náměstí 25 118 00 Praha 1, Czech Republic</addrLine>
              <country key="CZ"/>
            </address>
            <ref type="url">http://ktiml.mff.cuni.cz/index.php?select=home&amp;lang=english</ref>
          </desc>
          <listRelation>
            <relation active="#struct-304738" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-119123" status="INCOMING">
          <orgName>Oddelek za Matematiko</orgName>
          <desc>
            <address>
              <addrLine>Oddelek za Matematiko Fakulteta za matematiko in fiziko Univeza v Ljubljani Jadranska 19 1000 Ljubljana Slovenia.</addrLine>
              <country key="SI"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-302844" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-38374" status="VALID">
          <orgName>Faculty of Mathematics and Physics [Ljubljana]</orgName>
          <orgName type="acronym">UL | FMF</orgName>
          <date type="start">1995-01-01</date>
          <desc>
            <address>
              <addrLine>University of Ljubljana | Jadranska ulica 19, 1000 Ljubljana</addrLine>
              <country key="SI"/>
            </address>
            <ref type="url">https://www.fmf.uni-lj.si/en/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302844" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-304738" status="VALID">
          <idno type="IdRef">069566992</idno>
          <idno type="ISNI">000000012160811X</idno>
          <idno type="ROR">https://ror.org/024d6js02</idno>
          <idno type="Wikidata">Q31519</idno>
          <orgName>Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic] = Université Charles  [Prague, Republique tchèque]</orgName>
          <orgName type="acronym">UK</orgName>
          <date type="start">1348-01-01</date>
          <desc>
            <address>
              <addrLine>Ovocný trh 5Prague 1116 36Czech Republic</addrLine>
              <country key="CZ"/>
            </address>
            <ref type="url">http://www.cuni.cz</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-302844" status="VALID">
          <idno type="ROR">https://ror.org/05njb9z20</idno>
          <orgName>University of Ljubljana</orgName>
          <desc>
            <address>
              <addrLine>Kongresni trg 12, 1000 Ljubljana</addrLine>
              <country key="SI"/>
            </address>
            <ref type="url">https://www.uni-lj.si/eng/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>