{"43366":{"#nid":"43366","#data":{"type":"event","title":"Some recent results in topological graph theory","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE: \u003C\/strong\u003E Some recent results in topological graph theory\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E Dr. Hein van der Holst\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\n\u003C\/p\u003E\n\u003Cp\u003EEach graph can be embedded in 3-space. The problem becomes more interesting if we put restrictions on the type of embedding. For example, a linkless embedding of a graph is one where each pair of vertex-disjoint circuits has linking number equal to zero. The class of all graphs that have a linkless embedding is closed under taking minors. Robertson, Seymour, and Thomas gave the forbidden minors for this class of graphs. Open remained how to find a linkless embedding in polynomial time. In the talk we start with discussing an algorithm to find a linkless embedding.\n\u003C\/p\u003E\n\u003Cp\u003EInstead of embedding the graph in 3-space, we could also consider mapping properties of certain superstructures of the graph in 3-space, and, indeed, if this superstructure has not the right mapping properties in 3-space, see whether it has the right one in 4-space, etc. We introduced for a graph G a new graph parameter  (G), which is defined as the smallest d such that superstructures of G have a zero intersection mapping in d-space. The nicest property of this graph parameter is its independence of the superstructure and thus depends on the graph only.  For d = 2 and d = 3,  (G)   d if and only if G is outerplanar and planar, respectively.  The graphs G with  (G)    4 are exactly those that have a linkless embedding. In the second part of the talk we will discuss this new graph parameter. (This part is joint work with R. Pendavingh.)\n\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"Some recent results in topological graph theory","format":"limited_html"}],"field_summary_sentence":[{"value":"Some recent results in topological graph theory"}],"uid":"27187","created_gmt":"2009-10-12 20:37:57","changed_gmt":"2016-10-08 01:47:38","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2008-10-06T16:00:00-04:00","event_time_end":"2008-10-06T17:00:00-04:00","event_time_end_last":"2008-10-06T17:00:00-04:00","gmt_time_start":"2008-10-06 20:00:00","gmt_time_end":"2008-10-06 21:00:00","gmt_time_end_last":"2008-10-06 21:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[{"id":"5684","name":"graph"},{"id":"167164","name":"superstructures"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cstrong\u003EAnita  Race\u003C\/strong\u003E\u003Cbr \/\u003EH. Milton Stewart School of Industrial and Systems Engineering\u003Cbr \/\u003E\u003Ca href=\u0022http:\/\/www.gatech.edu\/contact\/index.html?id=ar9\u0022\u003EContact Anita  Race\u003C\/a\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}