ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 26(1) (2006) 41-48
DOI: 10.7151/dmgt.1299


Iztok Peterin

Faculty of Electrical Engineering and Computer Science
University of Maribor
Smetanova ulica 17, 2000 Maribor, Slovenia


Median graphs have many interesting properties. One of them is-in connection with triangle free graphs-the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the convex expansion procedure that characterizes planar median graphs.

Keywords: median graphs, planar graphs, expansion.

2000 Mathematics Subject Classification: 05C10, 05C75.


[1] M. Behzad and E.S. Mahmoodian, On topological invariants of the product of graphs, Canad. Math. Bull. 12 (1969) 157-166, doi: 10.4153/CMB-1969-015-9.
[2] B. Bresar, W. Imrich, S. Klavžar, H.M. Mulder and R. Skrekovski, Tiled partial cubes, J. Graph Theory 40 (2002) 91-103, doi: 10.1002/jgt.10031.
[3] V.D. Chepoi, Isometric subgraphs of Hamming graphs and d-convexity, (Russian) Kibernetika (Kiev) (1988) 6-9; translation in Cybernetics 24 (1988) 6-11.
[4] D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory (B) 14 (1973) 263-267, doi: 10.1016/0095-8956(73)90010-5.
[5] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (John Wiley & Sons, New York, 2000).
[6] W. Imrich, S. Klavžar and H.M. Mulder, Median graphs and triangle-free graphs, SIAM J. Discrete Math. 12 (1999) 111-118, doi: 10.1137/S0895480197323494.
[7] S. Klavžar and H.M. Mulder, Median graphs: characterization, location theory and related structures, J. Combin. Math. Combin. Comp. 30 (1999) 103-127.
[8] B. Mohar and C. Thomassen, Graphs on Surfaces (Johns Hopkins University Press, Baltimore, MD, 2001).
[9] H.M. Mulder, The structure of median graphs, Discrete Math. 24 (1978) 197-204, doi: 10.1016/0012-365X(78)90199-1.
[10] H.M. Mulder, The Interval Function of a Graph (Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980).
[11] H.M. Mulder, The expansion procedure for graphs, Contemporary methods in graph theory 459-477 Bibliographisches Inst. Mannheim, 1990.
[12] P.M. Winkler, Isometric embedding in products of complete graphs, Discrete Appl. Math. 7 (1984) 221-225, doi: 10.1016/0166-218X(84)90069-6.

Received 7 October 2004
Revised 21 April 2005