11 citations · 23 across the 10 of their papers we have counts for
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A survey on recurrence relations for the independence polynomial of hypergraphs
Martin Trinks
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several rec…
Polynomial reconstruction of the matching polynomial
Xueliang Li, Yongtang Shi, Martin Trinks
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, i…
An Abstraction of Whitney's Broken Circuit Theorem
Klaus Dohmen, Martin Trinks
We establish a broad generalization of Whitney's broken circuit theorem on the chromatic polynomial of a graph to sums of type where is a finite set…
The Merrifield-Simmons conjecture also holds for parity graphs
Martin Trinks
The Merrifield-Simmons conjectures states a relation between the distance of vertices in a simple graph and the number of independent sets, denoted as , in vertex-deleted…
A note on a Broken-cycle Theorem for hypergraphs
Martin Trinks
Whitney's Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the state…
Recurrence relations and splitting formulas for the domination polynomial
Tomer Kotek, James Preen, Frank Simon +2
The domination polynomial D(G,x) of a graph G is the generating function of its dominating sets. We prove that D(G,x) satisfies a wide range of reduction formulas. We show linear r…