For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, ...
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. In 1984, Akiyama et al. [1] stated the Linear Arboricity Conjecture...
Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T of TS are adjacent if T intersects T...
Oswin Aichholzer, Franz Aurenhammer, Clemens Hueme...
Abstract. Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations...
Christian Bachmaier, Franz-Josef Brandenburg, Wolf...
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....