Sentence examples for a proper triangulation of from inspiring English sources

Therefore H is a proper triangulation of G(M).

We show that G(M) Q is a proper triangulation of G(M).

Thus H ′ is a proper triangulation of G ′ (M), and because H is a proper minimal triangulation of G ′ (M) it must be that H ′  =  H.

Hence the F-edges must be edges of H, so G ′ (M) ⊆  H and H is a proper triangulation of G ′ (M).

A proper triangulation of the partition intersection graph G(M) is a chordal supergraph of G(M) such that every edge has endpoints with different colors.

Thus, any explicit analysis of the edges of G(M) or of a proper triangulation of G(M) is inadequate to speed up our approach.

For a clique tree T  , we label the node corresponding to K t by t to obtain a perfect phylogeny for M. Conversely, if M has a perfect phylogeny T, then the species in T define a set of additional edges to obtain a proper triangulation for G(M).

Each F-edge of G ′ (M) comes from a chordless cycle of length four on three colors (see Lemma 2.12), so this edge must appear in any proper triangulation of G(M).

That is, given a clique tree T   for a proper triangulation H of G(M), we label each node by its corresponding maximal clique.

A triangulation of a graph G is minimal if it does not have a proper subgraph that is also a triangulation of G. Theorem 2.3 can be restated in terms of proper minimal triangulations of G(M) because removing edges from a proper triangulation will preserve the coloring of the graph.

By Theorem 2.7, graph G ′ (M) has a proper triangulation and since G(M) is a subgraph of G ′ (M), G M) also has a proper triangulation.