Corrigendum for `The path-partition problem in block graphs

Information Processing Letters 83 (2002) 293

www.elsevier.com/locate/ipl

Corrigendum to “The path-partition problem in block graphs”

[Information Processing Letters 52 (1994) 317–322]

Gerard J. Chang

Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Recently, Wong [1] pointed out that Yan and Chang’s [2] linear-time algorithm for the path-partition problem for block graphs is not correct, by giving the following example. Suppose G is the graph consisting of a vertex w and a set of triangles{xi, yi, zi} such that each xi is adjacent to w for 1
i
k, where

k 3. Then p(G) = k − 1, but Yan and Chang’s

al-gorithm gives p(G)= 1. He also traced the algorithm for the graph in Fig. 2 of [2] in a different ordering to get an inconsistent value. He then gave a linear-time algorithm for the problem.

We clarify two things. First, Yan and Chang’s al-gorithm is correct except for a typo: the J should be

J∗ in line 18 of Algorithm PPN. This is because it applies Theorem 3 for the graph G, the composition

✩

SSII of original article: 0020-0190(94)00158-8.

E-mail address: (G.J. Chang).

1 _{Supported in part by the National Science Council under grant}

NSC89-2115-M009-037.

of G1, G2, . . . , Gt−1. With this typo revised, the example above is then not a counterexample.

Second, the method in [1], although correct, is much more complicated. Many involved concepts and cases are introduced. It is not clear how the algorithm can be implemented in linear time.

References

[1] P.-K. Wong, Optimal path cover problem on block graphs, Theoret. Comput. Sci. 225 (1999) 163–169.

[2] J.-H. Yan, G.J. Chang, The path-partition problem in block graphs, Inform. Process. Lett. 52 (1994) 317–322.

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