



01475nas a2200145   4500008004100000022001400041245007300055210006900128260001500197300001200212490000600224520104100230100001701271856004101288       2013                        eng d  a1551-305X00aEvasiveness of Graph Properties and Topological Fixed-Point Theorems0 aEvasiveness of Graph Properties and Topological FixedPoint Theor  c2013/05/16  a337-4150 v73 a<p><span style="font-family: &quot;Lucida Grande&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">Many graph properties (e.g., connectedness, containing a complete subgraph) are known to be difficult to check. In a decision-tree model, the cost of an algorithm is measured by the number of edges in the graph that it queries. R. Karp conjectured in the early 1970s that all monotone graph properties are evasive -- that is, any algorithm which computes a monotone graph property must check all edges in the worst case. This conjecture is unproven, but a lot of progress has been made. Starting with the work of Kahn, Saks, and Sturtevant in 1984, topological methods have been applied to prove partial results on the Karp conjecture. This text is a tutorial on these topological methods. I give a fully self-contained account of the central proofs from the paper of Kahn, Saks, and Sturtevant, with no prior knowledge of topology assumed. I also briefly survey some of the more recent results on evasiveness.</span></p>1 aMiller, Carl  uhttp://dx.doi.org/10.1561/0400000055