Abstract
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every algorithmic problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ 1,L ) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time. The concept of clique-width extends the one of treewidth since bounded treewidth implies bounded clique-width.
We give a complete classification of all graph classes defined by forbidden one-vertex extensions of the P 4 with respect to their clique-width. Our results extend and improve recently published structural and complexity results in a systematic way.
Research of the first author partially supported by Kent State University, Kent, Ohio, research of the third and fourth author partially supported by German Research Community DFG Br 1446-4/1
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References
H.-J. Bandelt, H.M. Mulder, Distance-hereditary graphs, J. Combin. Theory (B) 41 (1986) 182–208
A. Brandstädt, (P5,diamond)-Free Graphs Revisited: Structure, Bounded cliquewidth and Linear Time Optimization, Manuscript 2000; accepted for Discrete Applied Math.
A. Brandstädt, C.T. Hoàng, V.B. Le, Stability Number of Bull-and Chair-Free Graphs Revisited, Manuscript 2001; accepted for Discrete Applied Math.
A. Brandstädt, D. Kratsch, On the structure of (P5,gem)-free graphs, Manuscript 2001
A. Brandstädt, H.-O. Le, R. Mosca, Chordal co-gem-free graphs have bounded clique-width, Manuscript 2002
A. Brandstädt, H.-O. Le, R. Mosca, (Gem,co-gem)-free graphs have bounded clique-width, Manuscript 2002
A. Brandstädt, V.B. Le, J. Spinrad, Graph Classes: A Survey, SIAM Monographs on Discrete Math. Appl., Vol. 3, SIAM, Philadelphia (1999)
A. Brandstädt, H.-O. Le, J.-M. Vanherpe, Structure and Stability Number of (Chair, Co-P, Gem)-Free Graphs, Manuscript 2001
A. Brandstädt, S. Mahfud, Linear time for Maximum Weight Stable Set on (claw,co-claw)-free graphs and similar graph classes, Manuscript 2001; to appear in Information Processing Letters
A. Brandstädt, R. Mosca, On the Structure and Stability Number of P5-and Co-Chair-Free Graphs, Manuscript 2001; accepted for Discrete Applied Math.
A. Brandstädt, R. Mosca, On Variations of P4-Sparse Graphs, Manuscript 2001
D.G. Corneil, H. Lerchs, L. Stewart-Burlingham, Complement reducible graphs, Discrete Applied Math. 3 (1981) 163–174
D.G. Corneil, Y. Perl, L.K. Stewart, Cographs: recognition, applications, and algorithms, Congressus Numer. 43 (1984) 249–258
D.G. Corneil, Y. Perl, L.K. Stewart, A linear recognition algorithm for cographs, SIAM J. Computing 14 (1985) 926–934
B. Courcelle, J. Engelfriet, G. Rozenberg, Handle-rewriting hypergraph grammars, J. Comput. Syst. Sciences, 46 (1993) 218–270
B. Courcelle, J.A. Makowsky, U. Rotics, Linear time solvable optimization problems on graphs of bounded clique width, extended abstract in: Conf. Proc. WG’98, LNCS 1517 (1998) 1–16; Theory of Computing Systems 33 (2000) 125-150
B. Courcelle, S. Olariu, Upper bounds to the clique-width of graphs, Discrete Appl. Math. 101 (2000) 77–114
C. De Simone, On the vertex packing problem, Graphs and Combinatorics 9 (1993) 19–30
S. Földes, P.L. Hammer, Split graphs, Congress. Numer. 19 (1977), 311–315
J.-L. Fouquet, A decomposition for a class of (P5, P5)-free graphs, Discrete Math. 121 (1993) 75–83
J.-L. Fouquet, V. Giakoumakis On semi-P4-sparse graphs, Discrete Math. 165–166 (1997) 267–290
J.-L. Fouquet, V. Giakoumakis, H. Thuillier, F. Maire, On graphs without P5 and P5, Discrete Math. 146 (1995) 33–44
M.C. Golumbic, U. Rotics, On the clique-width of some perfect graph classes, Int. Journal of Foundations of Computer Science 11 (2000) 423–443
A. Hertz, On a graph transformation which preserves the stability number, Yugoslav Journal of Oper. Res., to appear
C.T. Hoàng, A Class of Perfect Graphs, Ms. Sc. Thesis, School of Computer Science, McGill University, Montreal (1983)
C.T. Hoàng, Perfect Graphs, Ph. D. Thesis, School of Computer Science, McGill University, Montreal (1985)
C.T. Hoàng, B. Reed, Some classes of perfectly orderable graphs, J. Graph Theory 13 (1989) 445–463
B. Jamison, S. Olariu, A unique tree representation for P4-sparse graphs, Discrete Appl. Math. 35 (1992), 115–129
V.V. Lozin, Conic reduction of graphs for the stable set problem, Discrete Math. 222 (2000) 199–211
N.V.R. Mahadev, U.N. Peled, Threshold Graphs and Related Topics, Annals of Discrete Mathematics 56 (1995)
J.A. Makowsky, U. Rotics, On the clique-width of graphs with few P4’s, Int. J. of Foundations of Computer Science 3 (1999) 329–348
R.H. Möhring, F.J. Radermacher, Substitution decomposition for discrete structures and connections with combinatorial optimization, Annals of Discrete Math. 19 (1984) 257–356
M. Yannakakis, The complexity of the partial order dimension problem, SIAM J. Algebraic and Discrete Methods 3 (1982) 351–358
I.E. Zverovich, I.I. Zverovich, Extended (P5,P5)-free graphs, Rutcor Research Report RRR 22-2001 (2001) http://rutcor.rutgers.edu/~rrr
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Brandstädt, A., Dragan, F.F., Le, HO., Mosca, R. (2002). New Graph Classes of Bounded Clique-Width. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_6
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DOI: https://doi.org/10.1007/3-540-36379-3_6
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