11 citations · 32 across the 7 of their papers we have counts for
7 papers
The tree of decomposition of a biconnected graph
Dmitri Karpov
The tree of decomposition of a -connected graph by a set of pairwise independent -vertex cutsets is defined as follows. The vertices of this tree are cutsets of…
Upper bound on the number of edges of an almost planar bipartite graph
Dmitri Karpov
Let be a bipartite graph without loops and multiple edges on vertices, which can be drawn on the plane such that any edge intersects at most one other edge. We prove t…
Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least~4
Dmitri Karpov
We prove that every connected graph with vertices of degree~1 and 3 and vertices of degree at least~4 has a spanning tree with at least ${1\over 3}t +{1\over 4}s+{3\over 2}…
The structure of decomposition of a triconnected graph
Dmitri Karpov, Alexey Pastor
We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a sim…
Spanning trees with many leaves: new lower bounds in terms of number of vertices of degree~3 and at least~4
D. V. Karpov
We prove, that every connected graph with vertices of degree 3 and vertices of degree at least~4 has a spanning tree with at least leaves, wher…
On proper colorings of hypergraphs
Nick Gravin, Dmitrii Karpov
Let be a hypergraph of maximal vertex degree , such that each its hyperedge contains at least vertices. Let . We prove that (i) The h…