  We introduce a compact pangenome representation based on an optimal
segmentation concept that aims to reconstruct founder sequences from a multiple
sequence alignment (MSA). Such founder sequences have the feature that each row
of the MSA is a recombination of the founders. Several linear time dynamic
programming algorithms have been previously devised to optimize segmentations
that induce founder blocks that then can be concatenated into a set of founder
sequences. All possible concatenation orders can be expressed as a founder
block graph. We observe a key property of such graphs: if the node labels
(founder segments) do not repeat in the paths of the graph, such graphs can be
indexed for efficient string matching. We call such graphs segment repeat-free
founder block graphs.
  We give a linear time algorithm to construct a segment repeat-free founder
block graph given an MSA. The algorithm combines techniques from the founder
segmentation algorithms (Cazaux et al. SPIRE 2019) and fully-functional
bidirectional Burrows-Wheeler index (Belazzougui and Cunial, CPM 2019). We
derive a succinct index structure to support queries of arbitrary length in the
paths of the graph.
  Experiments on an MSA of SAR-CoV-2 strains are reported. An MSA of size
$410\times 29811$ is compacted in one minute into a segment repeat-free founder
block graph of 3900 nodes and 4440 edges. The maximum length and total length
of node labels is 12 and 34968, respectively. The index on the graph takes only
$3\%$ of the size of the MSA.
