Behind us rose a dark and forbidding wood of giant arborescent ferns intermingled with the commoner types of a primeval tropical forest.
"At the Earth's Core" by Edgar Rice Burroughs
Behind us rose a dark and forbidding wood of giant arborescent ferns intermingled with the commoner types of a primeval tropical forest.
"At the Earth's Core" by Edgar Rice Burroughs
Eurybia argophylla, musk-tree of Tasmania, an arborescent Composite.
"More Letters of Charles Darwin Volume II" by Charles Darwin
An arborescent Acacia, in dense thickets, intercepted our course several times.
"Journal of an Overland Expedition in Australia" by Ludwig Leichhardt
The irregularities of surface and arborescent appearance are well shown.
"Scientific American Supplement, No. 288" by Various
Nothing but the signs of a sickly vegetation, nowhere arborescent.
"An Antarctic Mystery" by Jules Verne
The arborescent and phaenogamous forms of the coral are to be noticed.
"Lippincott's Magazine of Popular Literature and Science, Vol. XII, No. 28. July, 1873." by Various
I picked up the fruit of a Magnolia and Castanea, and observed an arborescent Leea.
"Journals of Travels in Assam, Burma, Bhootan, Afghanistan and TheNeighbouring Countries" by William Griffith
The vegetation of the plain consists mainly of bunch-grass, juniper, and tall, arborescent cacti.
"The Delight Makers" by Adolf Bandelier
There may be burns, vesications, and ecchymoses; arborescent markings are not uncommon.
"Aids to Forensic Medicine and Toxicology" by W. G. Aitchison Robertson
This, like the ivy, when it rises above the wall, becomes arborescent, and ceases to throw out tendrils.
"Chambers's Edinburgh Journal, No. 454" by Various
Arborescent: branching like the twigs of a tree.
"Explanation of Terms Used in Entomology" by John. B. Smith
They were a species of arborescent yucca, then unknown to botanists.
"The War Trail" by Mayne Reid
The collection of the museum is already rich in trunks of arborescent fern.
"Movement of the International Literary Exchanges, between France and North America from January 1845 to May, 1846" by Various
JERSEY, arborescent cabbages of, i.
"The Variation of Animals and Plants Under Domestication, Volume II (of 2)" by Charles Darwin
The view afforded, however, by a good vertical section of a well-developed colony or cushion is interestingly arborescent.
"The North American Slime-Moulds" by Thomas H. (Thomas Huston) MacBride
Usually the metal is arborescent, dendritic, filiform, moss-like or laminar.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 3" by Various
Occurs usually massive and very arborescent.
"The Elements of Blowpipe Analysis" by Frederick Hutton Getman
In South America also arborescent grasses abound in the dense forests of Chiloe, in lat.
"Principles of Geology" by Charles Lyell
The majority of these are shrubs, only a few becoming truly arborescent.
"Michigan Trees" by Charles Herbert Otis
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Our result uses a well-known relationship between the Euler tours and arborescences of an Eulerian graph.
The number of Euler tours of a random directed graph
An arborescence of a directed graph G = (V , E ) is a rooted spanning tree of G in which all arcs are directed towards the root.
The number of Euler tours of a random directed graph
We will use ARBS (G) to denote the set of arborescences of G and, for any v ∈ V , use ARBS (G, v) to denote the set of arborescences rooted at v .
The number of Euler tours of a random directed graph
For any given digraph G = (V , E ), the well-known Matrix-tree theorem shows that for any v ∈ V the number of arborescences into v ∈ V exactly equals the value of the (v , v)-cofactor of the Laplacian matrix of G (see, for example, ).
The number of Euler tours of a random directed graph
Colbourn et al. gave an algorithm allowing sampling of a random arborescence rooted at v to be carried out in the same time as counting all such arborescences.
The number of Euler tours of a random directed graph
We ﬁrst prove a useful combinatorial lemma; then in Theorem 2 we derive and prove exact expressions for the ﬁrst and second moments for the number of arborescences of σ(F ), when F is a conﬁguration drawn uniformly at random from Φd n .
The number of Euler tours of a random directed graph
Next, in Theorem 3, we condition on the event that σ(F ) is a simple graph, to derive close approximations for the ﬁrst and second moment, for the number of Arborescences, when G is a simple graph drawn uniformly at random from G d n .
The number of Euler tours of a random directed graph
We use Fact 1 and Fact 2 to prove the following lemma. and in the proofs of subsequent results, we will speak of a conﬁguration for an (in-directed) arborescence or forest.
The number of Euler tours of a random directed graph
A ⊂ F is an arborescence of F ∈ Φd n if σ (A) is an arborescence of σ(F ).
The number of Euler tours of a random directed graph
For a better understanding, let us mention that the arborescences are not necessarily spanning and each vertex of D belongs to exactly rM (S) arborescences.
Basic Packing of Arborescences
There exists an M-basic packing of arborescences in (D , S, π) if and only if π is M-independent and (D , S, π) is M-connected.
Basic Packing of Arborescences
If M is the free matroid and π places every element of S at a single vertex r of D then the problem of M-basic packing of arborescences and that of packing of spanning arborescences rooted at r coincide.
Basic Packing of Arborescences
Then {T ′ t } is an M-basic packing of arborescences in (D , S, π).
Basic Packing of Arborescences
Then, by Theorem 1.6, there exists an M-basic packing of arborescences in (D , S, π) which provides, by forgetting the orientation, an M-basic packing of rooted-trees in (G, S, π).
Basic Packing of Arborescences
For each root si ∈ B2 , there exists an arc of Ti that enters X and the arborescences are arc-disjoint, so we have ρD (X ) ≥ |B2 | = |B| − |B1 | ≥ rM (S) − rM (SX ) that is (D , S, π) is M-connected.
Basic Packing of Arborescences
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