We show that computing the lexicographically first four-coloring for planar graphs is p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this ...
We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounde...
We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...
Given a graph G, we say S V (G) is resolving if for each pair of distinct u, v V (G) there is a vertex x in S where d(u, x) = d(v, x). The metric dimension of G is the minimum c...