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» Bounds on the forcing numbers of bipartite graphs
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COMGEO
2007
ACM
14 years 11 months ago
Graph drawings with few slopes
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...
Vida Dujmovic, Matthew Suderman, David R. Wood
JGT
2008
107views more  JGT 2008»
14 years 11 months ago
On planar intersection graphs with forbidden subgraphs
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
János Pach, Micha Sharir
DM
2010
143views more  DM 2010»
14 years 11 months ago
Acyclic improper colourings of graphs with bounded maximum degree
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
Louigi Addario-Berry, Louis Esperet, Ross J. Kang,...
DM
2010
103views more  DM 2010»
14 years 11 months ago
Degree-bounded factorizations of bipartite multigraphs and of pseudographs
For d 1, s 0 a (d,d +s)-graph is a graph whose degrees all lie in the interval {d,d +1,...,d +s}. For r 1, a 0 an (r,r+1)-factor of a graph G is a spanning (r,r+a)-subgraph of...
Anthony J. W. Hilton
JGT
2007
68views more  JGT 2007»
14 years 11 months ago
Forcing highly connected subgraphs
A well-known theorem of Mader [5] states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. Solving a problem of Diestel [2], we ex...
Maya Jakobine Stein