Fig. 1

Examples of the four types of absorption. Each panel shows the edges along two paths: \(\psi ^p\) (red vertices inside a shaded rectangle) and \(\psi ^c\) (blue vertices inside a shaded rectangle) and an absorption edge \(e=\{(u^p, s^p),(u^c,s^c)\}\) (dashed line) between the parent unitig \(u^p\) and the child unitig \(u^c\). The graph being shown in each panel is cdBG(K), but only the absorption edge and the edges of \(\psi ^p\) and \(\psi ^c\) are shown. In this simple example, the unitigs of dBG(K) are just paths made of single vertices, and hence the vertices of cdBG(K) have labels of length \(k=3\). Each vertex is shown as a pointed rectangle with its label inside; we use the convention that the “zero” side of a vertex is the flat side on the left, and the “one” side is the pointy side on the right. At the bottom left of each panel, we show the spectrum-preserving string set (SPSS) \(spell(\{\psi ^p, \psi ^c\})\). At the bottom right, we show the enriched representation generated by our algorithm. Depending on the value of \(s^p\) and \(s^c\), four different cases can arise. When \(s^p = 1, s^c = 0\) (shown in A), \(pre(lab(u^c))\) is replaced with marker “\(+\)”, as it is same as \(suf(lab(u^p))\). When \(s^p = 1, s^c = 1\) (shown in B), \(pre(lab(u^c))\) is replaced by “−”, as it is same as the reverse complement of \(suf(lab(u^p))\). When \(s^p = 0, s^c = 0\) (shown in C), \(pre(lab(u^c))\) is replaced with “−”, as it is the same as the reverse complement of \(pre(lab(u^p))\). When \(s^p = 0, s^c = 1\) (shown in D), \(suf(lab(u^c))\) is replaced with “\(+\)”, as it is the same as \(pre(lab(u^p))\)