For graphs G and H, hom-complexity C(G;H) is the fewest H-colourable subgraphs covering G, and when H has equal clique and chromatic number it equals ceil(log_{χ(H)} χ(G)), recovering known formulas for ℓ-particity and bipartite dimension.
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(Injective) hom-complexity between graphs
For graphs G and H, hom-complexity C(G;H) is the fewest H-colourable subgraphs covering G, and when H has equal clique and chromatic number it equals ceil(log_{χ(H)} χ(G)), recovering known formulas for ℓ-particity and bipartite dimension.