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DM
2010
129views more  DM 2010»
14 years 12 months ago
Interpolating between bounds on the independence number
For a non-negative integer T, we prove that the independence number of a graph G = (V, E) in which every vertex belongs to at most T triangles is at least uV f(d(u), T) where d(u)...
Anett Boßecker, Dieter Rautenbach
INFOCOM
1993
IEEE
15 years 4 months ago
Power-Optimal Layout of Passive, Single-Hop, Fiber-Optic Interconnections Whose Capacity Increases with the Number of Stations
Passive, single-hop interconnections among N stations, each with several transmitters and receivers, provide a communication path between any two stations using one of the transmi...
Yitzhak Birk
JCT
2008
103views more  JCT 2008»
14 years 12 months ago
A bijective proof of Jackson's formula for the number of factorizations of a cycle
Factorizations of the cyclic permutation (1 2 . . . N) into two permutations with respectively n and m cycles, or, equivalently, unicellular bicolored maps with N edges and n whit...
Gilles Schaeffer, Ekaterina A. Vassilieva
ITA
2007
104views Communications» more  ITA 2007»
14 years 11 months ago
Automata, Borel functions and real numbers in Pisot base
This note is about functions f : Aω → Bω whose graph is recognized by a B¨uchi finite automaton on the product alphabet A × B. These functions are Baire class 2 in the Bair...
Benoit Cagnard, Pierre Simonnet
SIAMDM
2008
118views more  SIAMDM 2008»
14 years 11 months ago
Ramsey-Type Problem for an Almost Monochromatic K4
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n 2ck contains a K4 whose edges receive at most two colors. Th...
Jacob Fox, Benny Sudakov