6 citations · 18 across the 6 of their papers we have counts for
6 papers
Unimodality of the independence polynomials of non-regular caterpillars
Patrick Bahls, Bailey Ethridge, Levente Szabo
The independence polynomial of a graph is the polynomial in variable in which the coefficient on gives the number of independent subsets $S \subseteq…
On the Ramsey Numbers of Trees with Small Diameter
Patrick Bahls, T. Scott Spencer
We estimate the Ramsey number r(T) = r(T,T) for various trees T, obtaining a precise value for r(T) for a large number of trees of diameter 3. Furthermore we prove that all trees o…
Generalizing -goodness to ordered graphs
Jeremy F. Alm, Patrick Bahls, Kayla Coffey +1
It is known that the connected graphs that are -good for all are the trees. In this paper, we ask which ordered trees are order--good for all .
Relative hyperbolicity and right-angled Coxeter groups
Patrick Bahls
We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.
Rigidity of two-dimensional Coxeter groups
Patrick Bahls
A Coxeter system is called two-dimensional if its associated Davis complex is two-dimensional (equivalently, every spherical subgroup has rank less than or equal to 2). We prove th…
Automorphisms of Coxeter groups
Patrick Bahls
We compute Aut(W) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by remov…