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Let M be a set of taxa whose characters have at most three states.
(Lemmas 4.2, 4.3, 4.7 [ 3]) Let M be a set of input taxa with at most three states per character, and suppose G(M) is properly triangulatable.
[ 3] Given an input set M with at most three states per character (r ≤ 3), M admits a perfect phylogeny if and only if every subset of three characters of M admits a perfect phylogeny.
[ 3] For input M on at most three states per character (r ≤ 3), there is a three-state perfect phylogeny for M if and only if the partition intersection graph for every pair of characters is acyclic and every monochromatic pair of vertices in G(M) is separated by a legal minimal separator.
Let M be a set of input taxa with at most three states per character, and consider any three characters χ i, χ j, χ k in M. If the partition intersection graph G(χ i, χ j, χ k ) is properly triangulatable, then the only possible chordless cycles in G(χ i, χ j, χ k ) are chordless 4-cycles, with two colors appearing once and the remaining color appearing twice.
Similar(55)
Given a flow nucleotide, a state s can transition to at most two states, one where an incorporation occurs, denoted, and one where no incorporation occurs, denoted.
This expression shows that we have two terms corresponding to two forms of energy storage and, thus, at the most, two state variables, namely, ρ and v.
Here the fact that there are at most three interior steady states plays a crucial role.
It is shown that this system can admit at most nine steady state solutions.
Yafati belongs to a network of 474 trained community volunteers in the three states most affected by the crisis.
The resulting model has at most two interior steady states and the basins of attraction of the steady states are completely determined [6].
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