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 problem for the above classes was unknown. We prove that deciding isomorphism of the classes are GI complete.

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We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is 27 35 . The other is for undirected graphs and its approximation ratio is 7 8 −o(1). Both algorithms improve on the previous bests.

We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is 27 35 . The other is for undirected graphs and its approximation ratio is

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