4 papers
The number of trees in distance-hereditary graphs and their friends
Danila Cherkashin, Pavel Prozorov
Counting the number of spanning trees in specific classes of graphs has attracted increasing attention in recent years. In this note, we present unified proofs and generalizations…
On stability of weighted spanning tree degree enumerators
Danila Cherkashin, Pavel Prozorov
Our previous paper shows that the (vertex) spanning tree degree enumerator polynomial of a connected graph is a real stable polynomial (id est is non-zero if all variables have…
On stability of spanning tree degree enumerators
Danila Cherkashin, Fedor Petrov, Pavel Prozorov
We show that the spanning tree degree enumerator polynomial of a connected graph is a real stable polynomial if and only if is distance-hereditary.
On the minimal sum of edges in a signed edge-dominated graph
Danila Cherkashin, Pavel Prozorov
Let be a simple graph with vertices and -weights on edges. Suppose that for every edge the sum of edges adjacent to (including itself) is positive. Then…