A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the following classes: linear domino graphs, P4-t...

In this note, we prove that all 2× 2 monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain 2× 2 having two monotone cells in the same row.

“Pleasing to the eye” (Gen 3:6) – this is how Genesis describes forbidden fruit when Adam and Eve were trying apologise for eating it, as, since time of first people, beauty, or that which “pleasing eye”, has been admired. Christian Fathers, early Church, came up against problem although human body was unquestionably beautiful, question right attitude towards it particular concern them. One the...

Let k be a natural number. We introduce k-threshold graphs. We show that there exists anO(n) algorithm for the recognition of k-threshold graphs for each natural number k. k-Threshold graphs are characterized by a finite collection of forbidden induced subgraphs. For the case k = 2 we characterize the partitioned 2threshold graphs by forbidden induced subgraphs. We introduce restricted, and spe...

We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.