The Borodin–Kostochka conjecture says that for a graph G , if Δ (G) ≥ 9 , then χ (G) ≤ max { Δ (G) − 1 , ω (G) }. Cranston and Rabern in [SIAM J. Discrete. Math. 27 (2013) 534–549] proved the conjecture holding for K 1 , 3 -free graphs. In this paper, we prove that the conjecture holds for K 1 , 3 ¯ -free graphs, where K 1 , 3 ¯ denotes the complement of K 1 , 3. [ABSTRACT FROM AUTHOR]
We correct an error occurred in Lemma 10, and a couple of typos in the following paper P. Dulio, S.M.C. Pagani A rounding theorem for unique binary tomographic reconstruction , Discrete Appl. Math. 268 (2019) 54–69. The corrections do not alter anyone of the obtained results. [ABSTRACT FROM AUTHOR]