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» Crossing-critical graphs with large maximum degree
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SIROCCO
2000
15 years 2 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»
15 years 1 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»
13 years 3 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»
15 years 1 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
15 years 6 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...