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5 papers · 2 filters
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}…
Covers counting via Feynman Calculus
Maksim Karev
Let be a finite group. In this paper we present a tool for counting the number of principle -bundles over a surface. As an application, we express (non-standard) generating…
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 tight spherical designs
Gabriele Nebe, Boris Venkov
Let X be a tight t-design of dimension n for one of the open cases t=5 or t=7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to e…