3 citations · 12 across the 36 of their papers we have counts for
7 papers · 1 filter
Local boxicity
Louis Esperet, Lyuben Lichev
A box is the cartesian product of real intervals, which are either bounded or equal to . A box is said to be -local if at most of the intervals are bounded. In t…
A note on the Erdős-Szekeres theorem in two dimensions
Lyuben Lichev
Burkill and Mirsky, and Kalmanson, prove independently that, for every , there is a sequence of vectors in , which does not contain a subsequ…
On the minimum bisection of random -regular graphs
Lyuben Lichev, Dieter Mitsche
In this paper we give new bounds on the bisection width of random 3-regular graphs on vertices. The main contribution is a new lower bound of based on a first momen…
On the chromatic number of the preferential attachment graph
Lyuben Lichev
We prove that for every and every , the chromatic number of the preferential attachment graph is asymptotically almost surely equal to $m…
On the modularity of 3-regular random graphs and random graphs with given degree sequences
Lyuben Lichev, Dieter Mitsche
The modularity of a graph is a parameter that measures its community structure; the higher its value (between and ), the more clustered the graph is. In this paper we show t…
On the Decycling Number of -regular Random Graphs
Lyuben Lichev, Dieter Mitsche
The decycling number of a graph is the smallest number of vertices which can be removed from so that the resulting graph has no cycles. Bau, Wormald and Zhou conject…