http://openproblemgarden.org/op/star_chromatic_index_of_cubic_graphs Comments for "Star chromatic index of cubic graphs" en http://openproblemgarden.org/op/star_chromatic_index_of_cubic_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/dvorak_zdenek">Dvorak</a>; <a href="/category/mohar">Mohar</a>; <a href="/category/samal">Samal</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>The star chromatic index <img class="teximage" src="/files/tex/53fd352197225c7c3044c3a6a69516595beeb73b.png" alt="$ \chi_s&#039;(G) $" /> of a graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored.</p> <div class="envtheorem"><b>Question</b>&nbsp;&nbsp; Is it true that for every (sub)cubic graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, we have <img class="teximage" src="/files/tex/939fe757ce3282a8fdccc122ba21e224cf9edd92.png" alt="$ \chi_s&#039;(G) \le 6 $" />? </div> </tr></td> </table> </td> </tr> </table> Dvorak, Zdenek Mohar, Bojan Samal, Robert edge coloring star coloring Graph Theory http://openproblemgarden.org/op/star_chromatic_index_of_cubic_graphs#comment Tue, 16 Nov 2010 10:31:07 +0100 Robert Samal 37271 at http://openproblemgarden.org