Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe an alg...
We present a new algorithm to compute a subset S of vertices of a planar graph G whose removal partitions G into O(N/h) subgraphs of size O(h) and with boundary size O( h) each. ...
We study the properties of embeddings, multicommodity flows, and sparse cuts in minor-closed families of graphs which are also closed under 2-sums; this includes planar graphs, g...
Amit Chakrabarti, Alexander Jaffe, James R. Lee, J...
We show how to embed a 3-connected planar graph with n vertices as a 3-polytope with small integer coordinates. The coordinates are bounded by O(27.55n ). The crucial part is the ...
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...