caa a22 4500 445358629 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00493-011-2665-9 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2665-9 Engström Alexander Department of Mathematics, University of California, 94720, Berkeley, CA, USA aut A local criterion for Tverberg graphs [Elektronische Daten] [Alexander Engström] The topological Tverberg theorem states that for any prime power q and continuous map from a (d+1)(q−1)-simplex to ℝ d , there are q disjoint faces F i of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the same face F i . A graph with the same vertex set as the simplex, and with two vertices adjacent if they should not be in the same F i , is called a Tverberg graph if the topological Tverberg theorem still work. These graphs have been studied by Hell, Schöneborn and Ziegler, and it is known that disjoint unions of small paths, cycles, and complete graphs are Tverberg graphs. We find many new examples by establishing a local criterion for a graph to be Tverberg. An easily stated corollary of our main theorem is that if the maximal degree of a graph is D, and D(D+1)<q, then it is a Tverberg graph. We state the affine versions of our results and also describe how they can be used to enumerate Tverberg partitions. János Bolyai Mathematical Society and Springer Verlag, 2011 Combinatorica Springer-Verlag 31/3(2011-05-01), 321-332 0209-9683 31:3<321 2011 31 493 https://doi.org/10.1007/s00493-011-2665-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2665-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Engström Alexander Department of Mathematics, University of California, 94720, Berkeley, CA, USA aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/3(2011-05-01), 321-332 0209-9683 31:3<321 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer