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math.CO2007
Enumeration of paths and cycles and e-coefficients of incomparability graphs
Gus Wiseman
We prove that the number of Hamiltonian paths on the complement of an acyclic digraph is equal to the number of cycle covers. As an application, we obtain a new expansion of the ch…
math.CO2005
Set maps, umbral calculus, and the chromatic polynomial
Gus Wiseman
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a form…
math.CO2005
A partition of connected graphs
Gus Wiseman
We define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize…