We give an algorithm requiring O(c1/2 n) time to find an -optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edgele...
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...
We show an algorithm for constructing O(dn log n) area outerplanar straight-line drawings of n-vertex outerplanar graphs with degree d. Also, we settle in the negative a conjectur...
We prove that for any fixed r 2, the tree-width of graphs not containing Kr as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of the...
Fedor V. Fomin, Sang-il Oum, Dimitrios M. Thilikos