We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, a...
For a positive integer k and a graph G, the k-colour graph of G, Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joine...
Luis Cereceda, Jan van den Heuvel, Matthew Johnson
For a given connected graph G on n vertices and m edges, we prove that its independence number α(G) is at least ((2m+n+2) -((2m+n+2)2 -16n2 )½ )/8. Keywords : independence numbe...
In this paper a polynomial algorithm for the prime factorization of finite, connected nonbipartite graphs with respect to the cardinal product is presented. This algorithm also d...
Deciding whether an arbitrary graph admits a VLSI layout with unit-length edges is NP-complete [1], even when restricted to binary trees [7]. However, for certain graphs, the prob...