Graph Minor check - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T23:13:28Z http://mathoverflow.net/feeds/question/101982 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101982/graph-minor-check Graph Minor check unknown (google) 2012-07-11T19:06:00Z 2012-07-12T13:23:51Z <p>Are there any good algebraic/algorithmic tools available to check if a given graph \$H\$ is a minor of \$G\$ from the adjacency matrix of \$G\$?</p> http://mathoverflow.net/questions/101982/graph-minor-check/101990#101990 Answer by Timothy Chow for Graph Minor check Timothy Chow 2012-07-11T21:25:31Z 2012-07-12T13:23:51Z <p>There is a general implementation in <a href="http://ask.sagemath.org/question/543/graph-minor-code-too-slow-in-certain-situations" rel="nofollow">Sage</a>. However, the algorithm runtime grows exponentially in the size of \$H\$. If you have a particular small \$H\$ in mind, there may be more efficient implementations available.</p> <p><b>EDIT:</b> In the comments below, the OP clarifies that the only case of interest is \$H=K_5\$. For this special case, the best known algorithm is due to Bruce Reed and Zhentao Li, "Optimization and Recognition for K5-minor Free Graphs in Linear Time," LATIN 2008, LNCS 4957, pp. 206–215, 2008. Reed's website also has a <a href="http://cgm.cs.mcgill.ca/~breed/newk5free.ps" rel="nofollow">draft paper</a> with fuller algorithmic details. Unfortunately, this algorithm is very complicated and I don't know if it has been implemented; I'd recommend emailing the authors to ask.</p> <p>By the way, if you find yourself having to write your own code, there is an earlier and simpler (though asymptotically less efficient) algorithm due to P. J. McGuinness and A. E. Kezdy, "Sequential and parallel algorithms to find \$K_5\$ minor," SODA 1992, pp. 206–215.</p> http://mathoverflow.net/questions/101982/graph-minor-check/101998#101998 Answer by Igor Rivin for Graph Minor check Igor Rivin 2012-07-11T22:28:55Z 2012-07-11T22:28:55Z <p>A polynomial time algorithm for this is given in </p> <p>Robertson + Seymour, Graph minors. XIII. The disjoint paths problem, Journal of Combinatorial Theory, Series B, 63 (1995), pp. 65–110.</p>