Edge separators for graphs of bounded genus with applications
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چکیده
Many divide-and-conquer algorithms on graphs are based on finding a small set of vertices or edges whose removal divides the graph roughly in half. Applications include VLSI layouts [14], Gaussian elimination Cl.51 and graph embeddings [17]. Formally, a class of graphs hasf’(n) vertex (edge) separator if every n-vertex graph in the class has a vertex (edge) cutset of sizef(n) that divides the graph into two parts having no more than 2n/3 vertices. Lipton and Tarjan [ 161 proved that planar graphs have O(J) vertex separator. The genus of a graph is the minimum number of handles that must be added to a sphere so that the graph can be embedded in the resulting sphere with no crossing edges. Djidjev [7] and Gilbert et al. [9] proposed
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Edge Separators for Graphs of Bounded Genus with Applications
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