<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262011000200002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Weak Diameter and Cyclic Properties in Oriented Graphs]]></article-title>
<article-title xml:lang="es"><![CDATA[Diámetro débil y propiedades cíclicas en digrafos antisimétricos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[BRITO]]></surname>
<given-names><![CDATA[DANIEL]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[ORDAZ]]></surname>
<given-names><![CDATA[OSCAR]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[VARELA]]></surname>
<given-names><![CDATA[MARÍA TERESA]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Oriente  ]]></institution>
<addr-line><![CDATA[Cumaná ]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Central de Venezuela  ]]></institution>
<addr-line><![CDATA[Caracas ]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad Simón Bolívar  ]]></institution>
<addr-line><![CDATA[Caracas ]]></addr-line>
<country>Venezuela</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>12</month>
<year>2011</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>12</month>
<year>2011</year>
</pub-date>
<volume>45</volume>
<numero>2</numero>
<fpage>129</fpage>
<lpage>135</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262011000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262011000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262011000200002&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[We describe several conditions on the minimum number of arcs ensuring that any two vertices in a strong oriented graph are joining by a path of length at most a given k, or ensuring that they are contained in a common cycle.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Damos varias condiciones sobre el número mínimo de arcos que implican la existencia, para todo par de vértices en un digrafo antisimétrico fuertemente conexo de un camino de longitud a lo más un k dado, que los une o de un circuito que los contiene.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Weak diameter]]></kwd>
<kwd lng="en"><![CDATA[2-Cyclic]]></kwd>
<kwd lng="en"><![CDATA[Oriented graph]]></kwd>
<kwd lng="es"><![CDATA[Diamétro débil]]></kwd>
<kwd lng="es"><![CDATA[2-ciclíco]]></kwd>
<kwd lng="es"><![CDATA[digrafo antisimétrico]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">      <p> <b> <font size="4">     <center> Weak Diameter and Cyclic Properties in Oriented Graphs </center> </font> </b> </p>      <p> <b> <font size="3">     <center> Di&aacute;metro d&eacute;bil y propiedades c&iacute;clicas en digrafos antisim&eacute;tricos </center> </font> </b> </p>      <p>     <center> DANIEL BRITO<sup>1</sup>,  OSCAR ORDAZ<sup>2</sup>,  MAR&Iacute;A TERESA VARELA<sup>3</sup> </center> </p>      <p> <sup>1</sup>Universidad de Oriente, Cuman&aacute;, Venezuela. Email: <a href="mailto:britodaniel@cantv.net">britodaniel@cantv.net</a>     <br>  <sup>2</sup>Universidad Central de Venezuela, Caracas, Venezuela. Email: <a href="mailto:oscarordaz55@gmail.com">oscarordaz55@gmail.com</a>     <br>  <sup>3</sup>Universidad Sim&oacute;n Bol&iacute;var, Caracas, Venezuela. Email: <a href="mailto:mtvarela@usb.ve">mtvarela@usb.ve</a>     ]]></body>
<body><![CDATA[<br> </p>  <hr size="1">      <p> <b>     <center> Abstract </center> </b> </p>      <p> We describe several conditions on the minimum number of arcs ensuring that any two vertices in a strong oriented graph are joining by a path of length at most a given <i>k</i>, or ensuring that they are contained in a common cycle. </p>      <p> <b> Key words: </b> Weak diameter, <i>2</i>-Cyclic, Oriented graph. </p>  <hr size="1">  <i>2000 Mathematics Subject Classification: 05B10, 11B13.</i>  <hr size="1">      <p> <b>     <center> Resumen </center> </b> </p>      <p> Damos varias condiciones sobre el n&uacute;mero m&iacute;nimo de arcos que implican la existencia, para todo par de v&eacute;rtices en un digrafo antisim&eacute;trico fuertemente conexo de un camino de longitud a lo m&aacute;s un <i>k</i> dado, que los une o de un circuito que los contiene. </p>      <p> <b> Palabras clave: </b> Diam&eacute;tro d&eacute;bil, <i>2</i>-cicl&iacute;co, digrafo antisim&eacute;trico. </p>  <hr size="1">      <p> Texto completo disponible en <a href="pdf/rcm/v45n2/v45n2a02.pdf">PDF</a> </p>  <hr size="1">      ]]></body>
<body><![CDATA[<p> <b> <font size="3"> References </font> </b> </p>       <!-- ref --><p> &#91;1&#93; J. Bang-Jensen, 'Problems and Conjectures Concerning Connectivity, Paths, Trees and Cycles in Tournament-Like Digraphs', <i>Discrete Mathematics</i> <i>309</i>, 18 (2009), 5655-5667.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000024&pid=S0034-7426201100020000200001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;2&#93; J. Bang-Jensen and G. Gutin, <i>Digraphs. Theory, Algorithms and Applications</i>, Second edn, Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, United Kingdom,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000026&pid=S0034-7426201100020000200002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 2009. </p>      <!-- ref --><p> &#91;3&#93; J. Bang-Jensen, G. Gutin, and A. Yeo, 'Hamiltonian Cycles avoiding Prescribed Arcs in Tournaments', <i>Combin. Probab. Comput.</i> <i>6</i>, 3 (1997), 255-261.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000028&pid=S0034-7426201100020000200003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;4&#93; J. C. Bermond and B. Bollob&aacute;s, 'The Diameter of Graphs. A survey', <i>Congressus Numerantium</i> <i>32</i>,  (1981),    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000030&pid=S0034-7426201100020000200004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 3-27. </p>      <!-- ref --><p> &#91;5&#93; J. C. Bermond and C. Thomassen, 'Cycles in Digraphs. A Survey', <i>Journal of Graph Theory</i> <i>5</i>,  (1981),    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000032&pid=S0034-7426201100020000200005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 1-43. </p>      <!-- ref --><p> &#91;6&#93; B. Bollob&aacute;s and A. Scott, 'Separating Systems and Oriented Graphs of Diameter Two', <i>J. Combinatorial Theory B</i> <i>97</i>, 2 (2007), 193-203.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000034&pid=S0034-7426201100020000200006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;7&#93; J. A. Bondy and U. S. R. Murty, <i>Graph Theory with Applications</i>, Macmillan, London, United Kingdom,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000036&pid=S0034-7426201100020000200007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 1976. </p>      <!-- ref --><p> &#91;8&#93; O. Favaron and O. Ordaz, 'A Sufficient Condition for Oriented Graphs to be Hamiltonian', <i>Discrete Math.</i> <i>58</i>,  (1986), 243-252.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000038&pid=S0034-7426201100020000200008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;9&#93; G. Gutin, 'Cycles and Paths in Semicomplete Multipartite Digraphs, Theorems and Algorithms. A Survey', <i>Journal of Graphs</i> <i>19</i>,  (1995), 481-508.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000040&pid=S0034-7426201100020000200009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;10&#93; M. C. Heydemann and D. Sotteau, 'About Some Cyclic Properties in Digraphs', <i>J. Combinatorial Theory B</i> <i>38</i>, 3 (1985), 261-278.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000042&pid=S0034-7426201100020000200010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;11&#93; C. Thomassen, Long Cycles in Digraphs, 'Proc. London Math. Soc.', (1981), Vol. 3, p. 231-251.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000044&pid=S0034-7426201100020000200011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;12&#93; C. Thomassen, Edge-Disjoint Hamiltonian Paths and Cycles in Tournaments, 'Proc. London Math. Soc.', (1982), Vol. 3, p. 151-168.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000046&pid=S0034-7426201100020000200012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>  <hr size="1">      <center> <b>(Recibido en julio de 2010. Aceptado en agosto de 2011)</b> </center> <hr size="1">      <p> Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>: </p> <code><font size="2" face="verdana"> @ARTICLE{RCMv45n2a02,    <br>  &nbsp;&nbsp;&nbsp; AUTHOR &nbsp;= {Brito, Daniel and Ordaz, Oscar and Varela, Mar&iacute;a Teresa},    <br>  &nbsp;&nbsp;&nbsp; TITLE &nbsp; = {{Weak Diameter and Cyclic Properties in Oriented Graphs}},    <br>  &nbsp;&nbsp;&nbsp; JOURNAL = {Revista Colombiana de Matem&aacute;ticas},    ]]></body>
<body><![CDATA[<br> &nbsp;&nbsp;&nbsp; YEAR &nbsp;&nbsp; = {2011},    <br> &nbsp;&nbsp;&nbsp; volume &nbsp;= {45},    <br> &nbsp;&nbsp;&nbsp; number &nbsp;= {2},    <br> &nbsp;&nbsp;&nbsp; pages &nbsp; = {129--135}    <br> } </font></code>  <hr size="1"> </font>      ]]></body><back>
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