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math.CO2026
Pairwise Compatibility Representations of Multidimensional Grid Graphs
Sheikh Azizul Hakim, Md. Shamsuzzoha Bayzid
Pairwise compatibility graphs (PCGs) represent graph adjacency by an interval of leaf-to-leaf distances in a weighted tree. We study grid graphs under the PCG model and two natural…
math.CO2026
On Threshold Pairwise Compatibility Graphs
Sheikh Azizul Hakim, Md. Shamsuzzoha Bayzid
Pairwise Compatibility Graphs (PCGs) form a tree-metric graph class that originated in phylogeny and has since attracted sustained interest in graph theory. Several natural general…