Discussiones Mathematicae Graph Theory 33(1) (2013)
doi: 10.7151/dmgt.1675

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Hereditarnia is a popular area in modern Graph Theory. It is concerned with hereditary properties of graphs, i.e., sets of graphs closed under taking (induced) subgraphs. Its study was greatly influenced by the paper [2] of Borowiecki and Mihók and its progress was seriously underlined and further stimulated by the directional survey paper [1] that was written a few years later.

Workers in this area, lead by Mietek Borowiecki, Izak Broere and Peter Mihók, founded the Hereditarnia Club in March 1996. The many activities of the growing group of members of this club are described in its web page at http://hereditarnia.ics.upjs.sk/ and include 15 workshops since December 1998. These productive meetings have all been characterised by the friendly collaborative style of Club members. On the ''formal'' side there has been an ''election'' of a new President at each meeting with Mietek as first (and longest serving) president.

The word Hereditarnia cannot be found in any dictionary. It is a combination of the English word ''Heredity'' and the Polish suffix ''arnia'' which is used in Polish in the description of many pleasant places (e.g. Palmiarnia); hence the word Hereditarnia is meant to describe the pleasant world of hereditary properties of graphs!

It is our privilege and honour (on behalf of all active workers in Hereditarnia) as members and former presidents of Hereditarnia Club to contribute with these words to this special edition of Discussiones Mathematicae Graph Theory devoted to our friend Mietek Borowiecki on the occasion of his 70th birthday!

Izak Broere and Peter Mihók


M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanisin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50.
M. Borowiecki and P. Mihók, Hereditary properties of graphs, in V.R. Kulli, Ed., Advances in Graph Theory (Vishwa International Publication, Gulbarga, 1991) 41-68.