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Note that each color is assigned to exactly two vertices.
itself is globally rigid and shares exactly two vertices with the two neighboring petals and.
Thus, the total weight of hyperedges incident to three vertices or more is insignificant in comparison to edges that are incident to exactly two vertices.
Hence, C has exactly four vertices, with exactly two vertices each from X F and Y F. We will first show that z i ∉ C for any i∈ p. Assume that z i ∈ C for some i∈[ p].
If the alleles at the k loci trace back to two parental gametes as a consequence of recombination (c.f. Section 2.2), then split the vertex x into exactly two vertices v1 and v2, distributing the set of edges that used to be incident with x to v1 and v2.
If a connected graph has exactly two vertices of odd degree, then it has an Euler path.
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The Voronoi diagram can be represented as a graph with vertices corresponding to the circumcenters of the Delaunay tetrahedrons and edges present if two tetrahedrons share a common side (i.e., share exactly three vertices).
Boundary points are equidistant to exactly two sites, and vertices are equidistant to at least 3. Neighboring points are points whose associated Voronoi regions share a common boundary.
This procedure is applied to vertices with exactly two attached edges.
Simple paths through this graph, comprised of vertices with exactly two incident edges, represent runs of anchors that are consistently ordered and syntenic in two or more genomes.
A tree is a graph in which any two vertices are connected by exactly one path.
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