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» Induced Subgraphs of Bounded Degree and Bounded Treewidth
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GC
2011
Springer
14 years 4 months ago
Properly Edge-Coloured Subgraphs in Colourings of Bounded Degree
The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1 or a properly edge-coloured Kt is denoted by f(s, t). Its existence is guarant...
Klas Markström, Andrew Thomason, Peter Wagner...
WG
2005
Springer
15 years 2 months ago
Computing the Tutte Polynomial on Graphs of Bounded Clique-Width
The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. Th...
Omer Giménez, Petr Hlinený, Marc Noy
DAM
2008
108views more  DAM 2008»
14 years 9 months ago
On the complexity of the multicut problem in bounded tree-width graphs and digraphs
Given an edge- or vertex-weighted graph or digraph and a list of source-sink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices wh...
Cédric Bentz
SIAMDM
2008
115views more  SIAMDM 2008»
14 years 9 months ago
Rank-Width and Well-Quasi-Ordering
Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle...
Sang-il Oum
ARSCOM
2008
103views more  ARSCOM 2008»
14 years 9 months ago
Estimating the number of graphs containing very long induced paths
Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
Steven Butler