For a fixed arbitrary edge coloring, this note studies rainbow C5-saturation with a prescribed number s of pendant triangles. For saturated graphs on at least five vertices, the color-avoidance and attachment-clique framework of Xu, He and Lu gives the lower bound s(s+5)/2; for s>0, equality forces the host T_s. For every integer s >= 128, a three-color complete core with globally distinct fresh pendant colors gives a saturated coloring of that exact host, with 3s vertices and s(s+5)/2 edges. The manuscript also relates pendant-pair deletion to normalized lower limits for graphs with independent degree-two vertices. OpenAI Codex assisted with literature retrieval, proof development, checks, writing, code and document preparation; the manuscript records the AI assistance.
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Zihuan Xu (2026) studied this question.
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