21 citations · 40 across the 11 of their papers we have counts for
13 papers
Edge Contraction and Line Graphs
Hany Ibrahim, Peter Tittmann
Given a family of graphs , a graph is -free if any subset of does not induce a subgraph of that is isomorphic to any graph in …
Edge Contraction and Forbidden Induced Graphs
Hany Ibrahim, Peter Tittmann
A graph is -free if any subset of does not induce a subgraph of that is isomorphic to . Given a graph , we present sufficient and necessary conditions for a…
On the Activities and Partitions of the Vertex Subsets of Graphs
Kristina Dedndreaj, Peter Tittmann
Crapo introduced a construction of interval partitions of the Boolean lattice for sets equipped with matroid structure. This construction, in the context of graphic matroids, is re…
Graph Operations and Neighborhood Polynomials
Maryam Alipour, Peter Tittmann
The neighborhood polynomial of graph is the generating function for the number of vertex subsets of of which the vertices have a common neighbor in . In this paper, we i…
The Bipartition Polynomial of a Graph: Reconstruction, Decomposition, and Applications
Seongmin Ok, Peter Tittmann
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We sh…
Counting Dominating Sets of Graphs
Irene Heinrich, Peter Tittmann
Counting dominating sets in a graph is closely related to the neighborhood complex of . We exploit this relation to prove that the number of dominating sets of a grap…