2022/10/30 by Pavol Hell, Jing Huang, Hell, Pavol +3
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2210.16714
openalex publication_date 2022/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the class of strong cocomparability graphs, as the class of reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01, 10, which we call Slash. We provide an ordering characterization, a forbidden structure characterization, and a polynomial-time recognition algorithm, for the class. These results complete the picture in which in addition to, or instead of, the Slash matrix one forbids the Gamma matrix (which has rows 11, 10). It is well known that in these two cases one obtains the class of interval graphs, and the class of strongly chordal graphs, respectively. By complementation, we obtain the class of strong comparability graphs, whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the two-by-two identity submatrix. Thus our results give characterizations and algorithms for this class of irreflexive graphs as well. In other words, our results may be interpreted as solving the following problem: given a symmetric 0,1-matrix with 0-diagonal, can the rows and columns of be simultaneously permuted to avoid the two-by-two identity submatrix?