... is called the complete cd-index of [u, v], and it is denoted by
ψ
u,v
(c, d). Notice
that the complete cd-index of [u, v] is an encoding of the distribution of the descent sets
of each path ... including a characterization, of the complete cd-index
of dihedral intervals. Furthermore, we describe a method to compute the complete
cd-index of intervals in u...
... dual of G and let C be a cycle of G. Lemma 3.2 implies that the
subgraphs of H on either s ide of C are connected and, therefore, the edges of H dual to
the edges of C form a bond of H.
To complete ... of a set X and a set I of subsets of X so that:
1. I = ∅;
2. if I ∈ I and J ⊆ I, then J ∈ I;
3. for each Y ⊆ X, there is a maximal element of I contained in Y ;...
... +
1
2
.
Proof. Suppose that X is a complete cap. If x and y are distinct points of X, then the
order of x − y is at least p. By Lemma 2.2, the number of points on lines between x and
y is at ... lines through x and 0 is at most n
2
/3, and the number of points
on lines through x and (n/2, 0) is at most n
2
/6, so the number of points on lines through
two points of X,on...
... contradiction and we have the proof of (4).
Theorem 3.5. M(K
m,n
) = 3 · 2
m+n−2
− 2
m−2
+ 2 for 2 ≤ m ≤ n.
Proof. Let G = K
m,n
, V (G) = {u
1
, u
2
, · · · , u
m+n
} and f be a maximal IC-coloring of
G. ... the
colorings of vertices of G are distinct.
Proof. Suppose, to the contrary, there exist two distinct vertices u and v such that f(u) =
f(v). Now, depending on the distrib...
...
2
Department of
Biology, Memorial University of Newfoundland, St. John's, NL A1B 3X9, Canada and
3
University of British Columbia, Department of Earth and
Ocean Sciences, Department of Microbiology ... analysis of coastal
RNA virus communities. Science
2006, 312:1795-1798.
11. Koonin EV, Dolja VV: Evolution and taxonomy of positive-
strand RNA viruses – implicati...
... analysis of coastal
RNA virus communities. Science
2006, 312:1795-1798.
11. Koonin EV, Dolja VV: Evolution and taxonomy of positive-
strand RNA viruses – implications of comparative-analysis of
amino-acid-sequences. ... distance of 0.1. See Additional
file 2 for complete virus names and accession numbers.
Bayesian maximum likelihood trees of aligned RdRp amino acid sequenc...