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» Crossing-critical graphs with large maximum degree
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SIROCCO
2000
13 years 10 months ago
Lower bounds for (weak) sense of direction
A graph with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, but it has been conje...
Paolo Boldi, Sebastiano Vigna
SIAMDM
2008
97views more  SIAMDM 2008»
13 years 8 months ago
Large Nearly Regular Induced Subgraphs
For a real c 1 and an integer n, let f(n, c) denote the maximum integer f such that every graph on n vertices contains an induced subgraph on at least f vertices in which the max...
Noga Alon, Michael Krivelevich, Benny Sudakov
SODA
2012
ACM
213views Algorithms» more  SODA 2012»
11 years 11 months ago
Expanders are universal for the class of all spanning trees
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
DMTCS
2006
66views Mathematics» more  DMTCS 2006»
13 years 8 months ago
On randomly colouring locally sparse graphs
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...
Alan M. Frieze, Juan Vera
STACS
2004
Springer
14 years 2 months ago
Matching Algorithms Are Fast in Sparse Random Graphs
We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability ...
Holger Bast, Kurt Mehlhorn, Guido Schäfer, Hi...