329 citations
- Technion – Israel Institute of TechnologyIL3 papers
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14 papers · 1 filter
The saturation spectrum for antichains of subsets
Jerrold R. Griggs, Thomas Kalinowski, Uwe Leck +2
Extending a classical theorem of Sperner, we characterize the integers such that there exists a maximal antichain of size in the Boolean lattice , that is, the power s…
Defensive alliance polynomial
Hany Ibrahim
We introduce a new bivariate polynomial which we call the defensive alliance polynomial and denote it by da(G; x, y). It is a generalization of the alliance polynomial [Carballosa…
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…
Subset-Sum Representations of Domination Polynomials
Tomer Kotek, James Preen, Peter Tittmann
The domination polynomial D(G,x) is the ordinary generating function for the dominating sets of an undirected graph G=(V,E) with respect to their cardinality. We consider in this p…
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…
Proving properties of the edge elimination polynomial using equivalent graph polynomials
Martin Trinks
Averbouch, Godlin and Makowsky define the edge elimination polynomial of a graph by a recurrence relation with respect to the deletion, contraction and extraction of an edge. It ge…