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DM
2010
129views more  DM 2010»
15 years 6 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 10 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»
15 years 6 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»
15 years 6 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»
15 years 6 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