Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Lengths of tours and permutations on a vertex set of a convex polygon
Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
Two equivalent measures on weighted hypergraphs
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Impossibility of transformation of vertex labeled simple graphs preserving the cut-size order
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Three equivalent partial orders on graphs with real edge-weights drawn on a convex polygon
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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Let x0, x1, ..., xn-1 be vertices of a convex n-gon P in the plane, where, x0x1X2,.... ,xn-2xn-1 and xn-1x0 are edges of P. Let G = (N, E) be a multigraph, such that N = {0, 1,.....,n - 1}. Consider a graph-drawing of G such that each vertex i ∈ N corresponds xi and each edge (i, j) ∈ E is drawn by a straight line segment. Denote the sum of the lengths of the edges of G in such a drawing by Sp (G). If Sp (G) ≤ Sp (G') for any convex n-gon P, then we write as G ≥l G'. This paper shows two necessary and sufficient conditions of G ≥l G'. Moreover, these conditions can be calculated in polynomial time for any given G and G'.