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DM
1999
90views more  DM 1999»
13 years 10 months ago
Induced subgraphs of given sizes
We say (n, e) (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has an m-vertex spanned subgraph with f edges. For example, as Tur
Paul Erdös, Zoltán Füredi, Bruce ...
CPC
2004
136views more  CPC 2004»
13 years 10 months ago
On the Strong Chromatic Number
The strong chromatic number, S(G), of an n-vertex graph G is the smallest number k such that after adding kn/k-n isolated vertices to G and considering any partition of the vertic...
Penny E. Haxell
SIAMCOMP
2008
65views more  SIAMCOMP 2008»
13 years 10 months ago
Exact Algorithms for Treewidth and Minimum Fill-In
We show that the treewidth and the minimum fill-in of an n-vertex graph can be
Fedor V. Fomin, Dieter Kratsch, Ioan Todinca, Yngv...
CORR
2010
Springer
103views Education» more  CORR 2010»
13 years 11 months ago
On Graph Crossing Number and Edge Planarization
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
ARSCOM
2007
81views more  ARSCOM 2007»
13 years 11 months ago
Graphic Sequences with a Realization Containing a Friendship Graph
For any simple graph H, let σ(H, n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex...
Michael Ferrara, Ronald J. Gould, John R. Schmitt
ESA
2010
Springer
126views Algorithms» more  ESA 2010»
13 years 12 months ago
Determining Edge Expansion and Other Connectivity Measures of Graphs of Bounded Genus
In this paper, we show that for an n-vertex graph G of genus g, the edge expansion of G can be determined in time nO(g2 ) . We show that the same is true for various other similar ...
Viresh Patel
DAGSTUHL
2006
14 years 9 days ago
Very Large Cliques are Easy to Detect
It is known that, for every constant k 3, the presence of a k-clique (a complete subgraph on k vertices) in an n-vertex graph cannot be detected by a monotone boolean circuit usi...
Alexander E. Andreev, Stasys Jukna
STOC
1990
ACM
135views Algorithms» more  STOC 1990»
14 years 2 months ago
A Separator Theorem for Graphs with an Excluded Minor and its Applications
ions (Extended Abstract) Noga Alon Paul Seymour Robin Thomas Let G be an n-vertex graph with nonnegative weights whose sum is 1 assigned to its vertices, and with no minor isomorp...
Noga Alon, Paul D. Seymour, Robin Thomas