Coloring discrete pseudomanifolds

Basak, Biplab (Department of Mathematics, Indian Institute of Technology Delhi)
Doem, Vanny (Research Scholar at Indian Institute of Technology (IIT) Kharagpur.)
Nahak, Chandal (Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications

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.