BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Samir Shukla (Indian Institute of Technology Bombay) DTSTART:20200916T053000Z DTEND:20200916T063000Z DTSTAMP:20260423T021418Z UID:CATGT/11 DESCRIPTION:Title: H igher independence complexes of graphs\nby Samir Shukla (Indian Instit ute of Technology Bombay) as part of Applications of Combinatorics in Alge bra\, Topology and Graph Theory\n\n\nAbstract\nIn 2006\, Szabó and Tardos generalized the concept of independence complex by defining $r$-independe nce complex of a graph $G$ for any $r \\geq 1$. Independence complexes ha ve applications in several areas. The topology of independence complex is related to many combinatorial properties of the underlined graph. The $ r$-independence complex of $G$\, denoted Ind$_r(G)$\, is the simplicial co mplex whose simplices are those subsets $I \\subseteq V(G)$ such that each connected component of the induced subgraph $G[I]$ has at most $r$ vertic es.\n\nIn this talk\, we give a lower bound for the distance $r$-dominatio n number of the graph $G$ (which is a very well studied notion in graph th eory and a natural generalization of the domination number of the graph) i n terms of the homological connectivity of the Ind$_r(G)$. We also prove t hat Ind$_r(G)$\, for a chordal graph $G$\, is either contractible or homot opy equivalent to a wedge of spheres. Given a wedge of spheres\, we also p rovide a construction of a chordal graph whose $r$-independence complex ha s the homotopy type of the given wedge. This is a joint work with Anurag S ingh and Priyavrat Deshpande.\n LOCATION:https://researchseminars.org/talk/CATGT/11/ END:VEVENT END:VCALENDAR