Add to ORKGBy means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on n vertices chosen uniformly at random satisfies an estimate of the form s%-n(1 + o(1)), where s and % are computable constants, the values of which are approximately s ˜ 0.09063 and %-1 ˜ 2.08415. We obtain analogue results for subfamilies of series-parallel graphs including 2-connected series-parallel graphs, 2-trees, and series-parallel graphs with fixed excess
The history of counting the number of spanning trees dates back into the year 1842 in which the Germ...
We prove that if a tree T has n vertices and maximum degree at most ∆, then a copy of T can almost s...
In this paper, a parallel algorithm is given that, given a graph G = (V; E), decides whether G is a ...
By means of analytic techniques we show that the expected number of spanning trees in a connected la...
In [6] it is shown that every graph can be probabilistically embedded into a distribution over its s...
We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn ∼ g...
Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G wit...
We give an asymptotic expression for the expected number of spanning trees in a random graph with a...
Let d ≥ 3 be a fixed integer. We give an asympotic formula for the expected number of spanning trees...
We prove that the maximum degree Δn of a random series-parallel graph with n vertices satisfies Δn/...
This thesis examines the robustness of sparse graphs and hypergraphs with respect to containing copi...
The length of a tree-decomposition of a graph is the maximum distance between two vertices of a same...
Let n ~ < n2 <.- be possible orders of connected regular graphs of fixed degree k 2 3. For eac...
In this paper we propose a limit characterization of the behaviour of classes of graphs with respec...
The number of spanning trees in a (di-)graph (network) is an important, well-studied quantity. Most ...
The history of counting the number of spanning trees dates back into the year 1842 in which the Germ...
We prove that if a tree T has n vertices and maximum degree at most ∆, then a copy of T can almost s...
In this paper, a parallel algorithm is given that, given a graph G = (V; E), decides whether G is a ...
By means of analytic techniques we show that the expected number of spanning trees in a connected la...
In [6] it is shown that every graph can be probabilistically embedded into a distribution over its s...
We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn ∼ g...
Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G wit...
We give an asymptotic expression for the expected number of spanning trees in a random graph with a...
Let d ≥ 3 be a fixed integer. We give an asympotic formula for the expected number of spanning trees...
We prove that the maximum degree Δn of a random series-parallel graph with n vertices satisfies Δn/...
This thesis examines the robustness of sparse graphs and hypergraphs with respect to containing copi...
The length of a tree-decomposition of a graph is the maximum distance between two vertices of a same...
Let n ~ < n2 <.- be possible orders of connected regular graphs of fixed degree k 2 3. For eac...
In this paper we propose a limit characterization of the behaviour of classes of graphs with respec...
The number of spanning trees in a (di-)graph (network) is an important, well-studied quantity. Most ...
The history of counting the number of spanning trees dates back into the year 1842 in which the Germ...
We prove that if a tree T has n vertices and maximum degree at most ∆, then a copy of T can almost s...
In this paper, a parallel algorithm is given that, given a graph G = (V; E), decides whether G is a ...