2026/07/30 by Jinghua Deng
Mathematics · #math.CO
arxiv created 2026/07/30 · arxiv updated 2026/07/31
For an n-vertex graph G, let N(H3,G) be the number of injective labeled copies of the red-blue path H3 for which the two blue pairs are mapped to non-edges of G and the red pair is mapped to an edge of G. We determine the maximum limiting value of N(H3,G)/n4 and give an extremal construction, which is the disjoint union of a clique and an asymptotically regular graph. The proof uses weighted vertex quotients and degree-square tie-breaking. We thereby resolve the exceptional four-vertex case left open in the recent classification of non-complete red-blue graphs.