DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory

PDF

Discussiones Mathematicae Graph Theory 21(1) (2001) 293-301
DOI: 10.7151/dmgt.1151

AN ATTRACTIVE CLASS OF BIPARTITE GRAPHS

Rodica Boliac and Vadim Lozin

RUTCOR, Rutgers University
640 Bartholomew Rd. Piscataway NJ 08854-8003 USA
e-mail: (boliac,lozin)@rutcor.rutgers.edu

Abstract

In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.

Keywords: bipartite graphs, structural characterization, polynomial algorithm.

2000 Mathematics Subject Classification: 05C75.

References

[1] V.E. Alekseev, A polynomial algorithm for finding maximum stable sets in fork-free graphs, Discrete Analysis and Operations Research, Ser.1, 6 (4) (1999) 3-19 (in Russian).
[2] A. Brandstädt, The jump number problem for biconvex graphs and rectangle covers of rectangular regions, Lecture Notes in Computer Science 380 (1989) 68-77, doi: 10.1007/3-540-51498-8_7.
[3] K. Cameron, Induced matchings, Discrete Appl. Math. 24 (1989) 97-102, doi: 10.1016/0166-218X(92)90275-F.
[4] G. Chaty and M. Chein, Ordered matchings and matchings without alternating cycles in bipartite graphs, Utilitas Mathematica 16 (1979) 183-187.
[5] E. Dahlhaus, The computation of the jump number of convex graphs, Lecture Notes in Computer Science 831 (1994) 176-185, doi: 10.1007/BFb0019434.
[6] G. Fricke and R. Laskar, Strong matchings on trees, Congr. Numer 89 (1992) 239-243.
[7] M.C. Golumbic and M. Lewenstein, New results on induced matchings, Discrete Appl. Math. 101 (2000) 157-165, doi: 10.1016/S0166-218X(99)00194-8.
[8] A. Kötzig, Paare Hajös the Graphen, Casopis Pest. Mat. 88 (1963) 236-241.
[9] H. Müller, Alternating cycle free matchings in chordal bipartite graphs, Order 7 (1990) 11-21, doi: 10.1007/BF00383169.
[10] G. Steiner and L. Stewart, A linear time algorithm to find the jump number of 2-dimensional bipartite orders, Order 3 (1987) 359-367, doi: 10.1007/BF00340778.
[11] M. Zito, Linear time maximum induced matching algorithm for trees, Nordic J. Computing 7 (2000) 58-63.

Received 3 March 2001
Revised 19 May 2001