It is known that any chordal graph can be uniquely decomposed into simplicial components. Based on this fact, it is shown that for a given chordal graph, its automorphism group can be computed in O((c! · n)O(1)) time, where c denotes the maximum size of simplicial components and n denotes the number of nodes. It is also shown that isomorphism of those chordal graphs can be decided within the sa...

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other side, the relative complexity of the GI probl...

A graph G = (V,E) is a chordal probe graph if its vertices can be partitioned into two sets, P (probes) and N (non-probes), where N is a stable set and such that G can be extended to a chordal graph by adding edges between non-probes. We give several characterizations of chordal probe graphs, first, in the case of a fixed given partition of the vertices into probes and non-probes, and second, i...

Let G be a finite simple graph. From the pioneering work of R. P. Stanley it is known that the cycle matroid of G is supersolvable if and only if G is chordal. The chordal binary matroids are not in general supersolvable. Nevertheless we prove that every supersolvable binary matroid determines canonically a chordal graph.

A generalized chordal graph is characterized by some positive integer k 3, and whose each cycle of length greater than k has a chord. Several tractable and intractable problems on a k-chordal graph are considered. When k is a xed positive integer, the recognition problem for k-chordalness is in NC. On a k-chordal graph, the maximal acyclic set problem is in NC when k = 3, and the problem is in ...

In this paper, we introduce the class of chordal probe graphs which are a generalization of both interval probe graphs and chordal graphs. A graph G is chordal probe if its vertices can be partitioned into two sets P (probes) and N (non-probes) where N is a stable set and such that G can be extended to a chordal graph by adding edges between non-probes. We show that chordal probe graphs may con...

In 1995 Golumbic, Kaplan and Shamir defined graph sandwich problems as follows: graph sandwich problem for property Π (Π-sp) Input: Two graphs G = (V,E) and G = (V,E) such that E ⊆ E. Question: Is there a graph G = (V,E) satisfying the property Π such that E ⊆ E ⊆ E? The graphG is called sandwich graph for the pair (G, G). Note that making E = E = E we have the recognition problem for the prope...

Let G be a connected graph with the usual shortest-path metric d. The graph G is δ-hyperbolic provided for any vertices x, y, u, v in it, the two larger of the three sums d(u, v) + d(x, y), d(u, x) + d(v, y) and d(u, y) + d(v, x) differ by at most 2δ. The graph G is k-chordal provided it has no induced cycle of length greater than k. Brinkmann, Koolen and Moulton find that every 3-chordal graph...

An efficiently total dominating set of a graph G is a subset of its vertices such that each vertex of G is adjacent to exactly one vertex of the subset. If there is such a subset, then G is an efficiently total dominable graph (G is etd). In this paper, we prove NP-completeness of the etd decision problem on the class of planar bipartite graphs of maximum degree 3. Furthermore, we give an effic...

The mirror (or bipartite complement) mir(B) of a bipartite graph B = (X,Y,E) has the same color classes X and Y as B, and two vertices x ∈ X and y ∈ Y are adjacent in mir(B) if and only if xy / ∈ E. A bipartite graph is chordal bipartite if none of its induced subgraphs is a chordless cycle with at least six vertices. In this paper, we deal with chordal bipartite graphs whose mirror is chordal ...