Coloring discrete pseudomanifolds - Biplab Basak; Vanny Doem; Chandal Nahak (Electronic Journal of Graph Theory and Applications (EJGTA), 2026)
This paper presents three main results concerning the coloring of discrete d-pseudomanifolds: (1) the general chromatic bounds d+1 ≤ X(K) ≤ 2d+2 for any d-pseudomanifold K; (2) an improved bound X(K) ≤ 2d+1 for a d-pseudomanifold expressible as a join K = Sk + K', where Sk is a cyclic k-sphere and K' is a subpseudomanifold; (3) the optimal bound X(K) ≤ ⌈3(d+1)/2⌉, where ⌈-⌉ is a ceiling function, under the additional assumptions that the spherical join factor Sk is an even-cyclic k-sphere and its dimension k is sufficiently close to d.