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math.CO2005★ 1 cited
Colourful Simplicial Depth
Antoine Deza, Sui Huang, Tamon Stephen +1
Inspired by Barany's colourful Caratheodory theorem, we introduce a colourful generalization of Liu's simplicial depth. We prove a parity property and conjecture that the minimum c…
math.CO2004★ 2 cited
A majorization bound for the eigenvalues of some graph Laplacians
Tamon Stephen
It is conjectured that the Laplacian spectrum of a graph is majorized by its conjugate degree sequence. In this paper, we prove that this majorization holds for a class of graphs i…
math.CO2004★ 2 cited
Local chromatic number, Ky Fan's theorem, and circular colorings
Gabor Simonyi, Gabor Tardos
The local chromatic number of a graph was introduced by Erdos et al. in 1986. It is in between the chromatic and fractional chromatic numbers. This motivates the study of the local…