Edge isoperimetric problems on graphs
WebDiscrete Isoperimetric Inequalities Fan Chung University of California at San Diego La Jolla, CA 92093-0112 1 Introduction One of the earliest problems in geometry is the isoperimetric problem, which was considered by the ancient Greeks. The problem is to nd, among all closed curves of a given length, the one which encloses the maximum area. Webstandard graph invariant appearing e.g. in the linear VLSI layouts [20], and is related to such a classical topic like the discrete isoperimetric problem [1]. We prove cr(G)+ 1 16 v∈G d2 v ≥ 1 1176 cw2(G). Regardless the constant factors, the improvement is evident as cw(G) ≥ bw(G) and there are connected graphs with bw(G) = 1 but with ...
Edge isoperimetric problems on graphs
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WebSep 25, 2011 · In this paper we solve the edge isoperimetric problem for folded hypercubes and thereby obtain the exact wirelength of folded hypercubes into paths. ... Das S.K., Elsässer R.: An edge-isoperimetric problem for powers of the Petersen graph. Ann. Comb. 4, 153–169 (2000) Article MathSciNet MATH Google Scholar Boals A.J., Gupta … Webn be the graph with vertex set {−1,1}n in which two vertices are joined if their Hamming distance is at most r. The edge-isoperimetric problem for Qr ... The edge-isoperimetric problem is also related to the estimate of distance distribution of a subset in the hypercube Qn. For a graph G= (V,E) and a non-empty subset A⊆V, the ...
WebDec 26, 1997 · We survey results on edge isoperimetric problems on graphs, present some new results and show some applications of such problems in combinatorics and computer science. 1 Introduction Let G = (VG ... WebOct 14, 2003 · Abstract. We consider an edge-isoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for …
WebAs a corollary of our result, together with isoperimetric inequalities, we close these exponential gaps giving asymptotically optimal bounds on long paths in hypercubes, discrete tori, and more generally Hamming graphs. WebThe following edge isoperimetric problems are used as tools to solve the MinLA problem. MinLA has been computed for regular graphs such as hypercubes [4], circulant graphs [8], folded hypercubes ...
WebMar 19, 2024 · Liu et al. use the edge isoperimetric problem to determine the exact wirelengths of embedding an enhanced hypercube into windmill and necklace graphs by partitioning the edge set of the host graph. The results obtained in this paper may have a great impact on parallel computing systems.
WebPáles , Problem in report of meeting, the forty-first international symposium on functional equations, Aequationes Math., 67 ( 2004), pp. 285 -- 320 . Google Scholar Keywords redneck wine tastingWebThe generalised Johnson graphs are the graphs J(n, k, m) whose vertices are the k subsets of {1, 2, . . . , n}, with two vertices J1 and J2 joined by an edge if and only if … richard woelfel racineWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We survey results on edge isoperimetric problems on graphs, present some new results and … redneck with overallsWebEdge isoperimetric problems on graphs. Graph theory and combinatorial biology, 7:157{197, 1999. [15]S. L. Bezrukov and R. Els asser. Edge-isoperimetric problems … redneck with bad teethWebAbstract. It is shown that there exists a linear ordering of the points in I + n or I n (Cartesian products of nonnegative integers or integers) such that the first j points in this ordering is … richard wochinger facebookWebIsoperimetric problems 2.1. History One of the earliest problems in geometry was the isoperimetric problem, which was considered by the ancient Greeks. The problem is … redneck with no teethWebfrom analysis. There are two discrete versions of this problem in graph theory: the vertex isoperimetric problem and the edge isoperimetric problem. In both problems, we wish to minimize the \boundary" of a vertex subset of a given size. For a simple graph G= (V;E) and vertex subset A V, the vertex boundary is the set @A= fv2VnA: vadjacent to ... richard wobby jewelers