Morimasa Tsuchiya

On upper bound graphs whose complements are also upper bound graphs

Abstract In this paper, we consider upper bound graphs and double bound graphs of posets. We obtain a characterization of upper bound graphs whose complements are also upper bound graphs as follows: for a connected graph G, both G and G are upper bound graphs if and only if G is a split graph with V(G) = K + S, where K is a clique and S is an independent set, satisfying one of the following conditions: 1. (1) there exists a vertex in K with no neighbour in S, or 2. (2) for each edge e = uv in K, there exists a vertex w ∈ S such that u, v ∈ N(w), and for each pair of vertices x, y ∈ S, there exists a vertex v ∈ K such that neither x nor y is adjacent to v. We also obtain some properties of double bound graphs of height one posets.

On upper bound graphs with respect to operations on graphs

We consider upper bound graphs with respect to unary operations on graphs, that is, line graphs, middle graphs, total graphs and squares of graphs. According to the characterization of upper bound graphs, we deal with characterizations of upper bound graphs obtained by graph operations of upper bound graphs. For example, the line graph of a connected upper bound graph G is an upper bound graph if and only if G = K 3 or G = K 1 +H, where \( H = mK_1 \bigcup nK_2 (m \geq 1, n \geq 0) \) and the square of an upper bound graph G is an upper bound graph if and only if the in tersection graph of the corresponding edge clique cover of G is an upper bound graph.

On transformation of posets which have the same bound graph

Abstract In this paper, we consider transformations between posets P and Q , whose double bound graphs are the same. We obtain that P can be transformed into Q by a finite sequence of two transformations, that is, d_addition and d_deletion on posets. This result induces a characterization on unique double bound graphs. Furthermore, we show some properties on minimal posets and maximal posets whose double bound graphs are the same.

A note on chordal bound graphs and posets

We study relations between induced subgraphs and (n,m)-subposets. Using properties of (n,m)-subposets, we consider a characterization of chordal double bound graphs in terms of forbidden subposets. Furthermore, we deal with properties of a poset whose double bound graph is isomorphic to its upper bound graph or its comparability graph, etc.

On antichain intersection numbers, total clique covers and regular graphs

In this paper, we consider total clique covers and intersection numbers on multifamilies. We determine the antichain intersection numbers of graphs in terms of total clique covers. From this result and some properties of intersection graphs on multifamilies, we determine the antichain intersection numbers of 3-, 4-, 5-regular graphs and some special graphs.

Structure of the food web including the endangered lycaenid butterfly Shijimiaeoides divinus asonis (Lepidoptera: Lycaenidae)

The structure of the food web including the endangered lycaenid butterfly Shijimiaeoides divinus asonis (Matsumura) was analyzed to identify species contributing most to maintaining the equilibrium of the food web. Twenty‐seven species belonging to 17 families fed on Sophora flavescens Aiton, the host‐plant of S. divinus asonis: 15 species were leaf and stem feeders, seven (including S. divinus asonis) fed on flower buds, four were flower feeders and one fed on the seeds of So. flavescens. Of these 27 species, four were omnivores. The natural enemies of S. divinus asonis comprised six insect species, 11 spider species and one entomopathogenic fungus species, including six new predator records. The linkage density, total number of trophic links, connectance, average chain length and predator–prey ratio were 1.617, 97, 0.0548, 2.267 and 0.694, respectively. Exclusion of any of the 15 species with four or more trophic links reduced the connectance of the food web. These 15 species included facultative mutualistic attendant ants and predators of S. divinus asonis, herbivores to So. flavescens, an omnivore feeding on S. divinus asonis and So. flavescens, and prey insects. Therefore, future studies should monitor these 15 species.

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.

On Double Bound Graphs with Respect to Graph Operations

We consider upper bound graphs with respect to operations on graphs, for example, the sum, the Cartesian product, the corona and the middle graphs of graphs, etc. According to the characterization of double bound graphs, we deal with characterizations of double bound graphs obtained by graph operations. For example, The Cartesian product G × Hof two graphs G and H is a DB-graph if and only if both G and H are bipartite graphs, the corona G ? Hof two graphs Gand His a DB-graph if and only if Gis a bipartite graph and H is a UB-graph, and the middle graph M(G)of a graph Gis a DB-graph if and only if G is an even cycle or a path, etc.

On construction of bound graphs

Abstract In this talk, we consider construction of double bound graphs. A double bound graph can be transformed into a bipartite graph by deletions and a bipartite graph also can be transformed into a double bound graph by additions. These results induce a characterization on double bound graphs.