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The genes of π, denoted g, form a matching on V such that g ⊆ G ; the adjacencies of π, denoted a, form a matching on V g. We color the genes of π black and the adjacencies of π blue (see Figure 1(a)).
Introducing the symbol MWM for the maximum weight of a matching on the auxiliary graph Γ, we can write this as (7) Here we make use of the fact that the weight of a matching equals the sum of the weights of the path-systems that correspond to the edges of the auxiliary graphs.
We can thus recognize adjacencies between these contig projections in each summary genome and carry out MWM, using the same weights as in Table 3 in Step 3 and the deletions in Step 4 to construct a new median consisting of a matching on the contigs.
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