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, ...
A connected graph G is called t-perfect if its stable set polytope is determined by the non-negativity, edge and odd-cycle inequalities. Moreover, G is called strongly t-perfect i...
A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number is the minimum...
Let ir(G) and (G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H) = (H), for every induced subgr...
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolati...