Satoshi Tagusari

On strict-double-bound numbers of caterpillars

For a poset P = (X, ≤P), the strict-double-bound graphsDB(P) is the graph on X for which vertices u and v of sDB(P) are adjacent if and only if u ≠ v and there exist x and y in X distinct from u and v such that x ≤ P u ≤ P y and x ≤ P v ≤ P y. The strict-double-bound numberζ(G) of a graph G is defined as is a strict-double-bound graph}. We obtain that for a caterpillar Catn(m,m,…,m)(n ≥ 3). We also have that for

On upper bound graphs with forbidden subposets

Abstract For a poset P = ( X , ⩽ P ) , the upper bound graph (UB-graph) of P is the graph U B ( P ) = ( X , E U B ( P ) ) , where x y ∈ E U B ( P ) if and only if x ≠ y and there exists m ∈ X such that x , y ⩽ P m . We show some characterizations on split upper bound graphs, threshold upper bound graphs and difference upper bound graphs in terms of m-subposets and canonical posets.