We extend and generalise Sergiescu's results on planar graphs and presentations for the braid group Bₙ to other topological generalisations of Bₙ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-1, author = {Paolo Bellingeri and Vladimir Vershinin}, title = {Presentations of surface braid groups by graphs}, journal = {Fundamenta Mathematicae}, volume = {185}, year = {2005}, pages = {1-20}, zbl = {1165.20030}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-1} }
Paolo Bellingeri; Vladimir Vershinin. Presentations of surface braid groups by graphs. Fundamenta Mathematicae, Tome 185 (2005) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm188-0-1/