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An analogous statement for rooted element-connectivity was proved by Király and Lau <ref name="KiLa"/>. A directed graph ''D'' with terminal set ''T'' is '''rooted ''k''-element-connected''' from <math>r \in T</math> if there are ''k'' element-disjoint paths from ''r'' to any other node in ''T''. It is NP-complete to decide if a graph has a rooted ''k''-element-connected orientation<ref name="KiLa"/>, but Király and Lau proved that if the graph is ''2k''-element-connected, then for any root <math>r \in T</math> it has a rooted ''k''-element-connected orientation.
Cheriyan and Zou <ref name="ChZo"/> proved the conjecture for incidence graphs of projective planes, where the terminal set is one side of the bipartition.An important related result is the characterization of graphs having a 2-connected orientation by Thomassen <ref name="Th"/>, see also [[Characterization of graphs having a k-connected orientation]].
==References==
<references>
<ref name="KiLa">T. Király, L.C. Lau, ''Approximate min-max theorems for Steiner rooted-orientations of graphs and hypergraphs'', Journal of Combinatorial Theory B 98 (2008), 1233-1252. [http://dx.doi.org/10.1016/j.jctb.2008.01.006 DOI link], [http://www.cs.elte.hu/egres/tr/egres-06-13.pdf EGRES Technical Report no. 2006-13]</ref>
<ref name="ChZo">J. Cheriyan, C. Zou, ''On orienting graphs for connectivity: Projective planes and Halin graphs'', Operations Research Letters 40 (2012), 337–341, [http://dx.doi.org/10.1016/j.orl.2012.06.004 DOI link]</ref> <ref name="Th">C.Thomassen, ''Strongly 2-connected orientations of graphs'', JCTB 110 (2015), 67-78, [http://dx.doi.org/10.1016/j.jctb.2014.07.004 DOI link]</ref>
</references>
