In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. T...
: We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured b...
It is shown that in a 4-connected maximal planar graph there is for any four vertices a, b, c and d, a cycle in the graph that contains the four vertices and visits them in the or...
We prove that, for every two n-node non-star trees of diameter at most four, there exists an n-node planar graph containing them as edge-disjoint subgraphs.
We consider the problem of finding obnoxious centers in graphs. For arbitrary graphs with n vertices and m edges, we give a randomized algorithm with O(n log2 n + m log n) expecte...