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Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz
Chromatic number clique subdivisions Hajos and Erdos-Fajtlowicz Combinatorics
2011/9/1
Abstract: For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all ...
Random walks on barycentric subdivisions and the Strichartz hexacarpet
Random walks barycentric subdivisions the Strichartz hexacarpet
2011/7/29
Abstract: We investigate the relation between simple random walks on repeated barycentric subdivisions of a triangle and a self-similar fractal, Strichartz hexacarpet, which we introduce. We explore a...
The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided K5 .
We investigate subdivisions of simplicial, cyclic, and dihedral sets by using Drinfeld’s expression of geometric realization as a filtered colimit.
On the dimension of spline spaces on planar T-subdivisions
spline spaces planar T-subdivisions
2010/11/12
We analyze the space S_{m, m'}^{r, r'} (T) of bivariate functions that are piecewise polynomial of bidegree (m, m') and class C^{r, r'} over a planar T-subdivision. We give a new formula for the dime...