�� <!DOCTYPE html> <html> <head> <style type="text/css"> body { font-family:Verdana; background-color:#F5F5F5; } div.horizontal { } div.horizontal ul { list-style-type:none; margin:0; padding:0; border-width:0px; } div.horizontal li { float:left; width:14.28%; } div.horizontal a { display:block; } div.horizontal a:link,div.horizontal a:visited { font-weight:bold; color:#111111; background-color:#FFFFFF; text-align:center; padding-bottom:19px; padding-top:19px; text-decoration:none; width:100%; } div.horizontal a:hover,div.horizontal a:active { background-color:#FFD433; } div.initbox { display:block; font-weight:bold; font-size:26px; color:#FFFFFF; background-color:#5D5D5D; text-align:center; padding-bottom:10px; padding-top:20px; text-decoration:none; } #thispage { background-color:#FFC300; } </style> <title>Combinatorics</title> <script type="text/javascript" async src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML"> </script> </head> <body> <div class="initbox">Combinatorial group</div> <div class="horizontal"><ul> <li><a href="index.html" >Main page</a></li> <li><a href="people.html">People</a></li> <li><a href="seminar.html" id="thispage">Seminar </a></li> <li><a href="events.html">Events</a></li> <li><a href="students.html">Openings</a></li> <li><a href="outputs.html">Outputs</a></li> <li><a href="fundings.html">Funding</a></li> </ul> </div> <!-- Math code: <img src="http://latex.codecogs.com/gif.latex? THE CODE " border="0"/> --> <p style="color:red;"><b>A note to visitors:</b> a recent negative test is needed to enter the institute; please read the <a href="covid.pdf">regulations</a> (search for word "Guests"). It is also possible to self-test at the institute, hence please arrive at least 20 mins before the talk.</p> <hr> <h2>Programme</h2> <p><b> Monday 14.3.2022 at 10:00 <a href="http://www.ustavinformatiky.cz/">ICS</a>, room TBA, <a href="http://honza.ucw.cz/">Jan Volec</a> (Czech Technical University): TBA</b></p> <p><b> Monday 14.2.2022 at 10:00 <a href="http://www.ustavinformatiky.cz/">ICS</a>, room 419, <a>Eng Keat Hng</a> (ICS CAS): Minimum degree conditions for powers of cycles and paths</b></p> <p><u>Abstract</u>: We study minimum degree conditions under which a graph G contains kth powers of paths and cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of $G$ is large. This extends a result of Allen, B�ttcher and Hladk� [J. Lond. Math. Soc. (2) 84(2) (2011), 269--302] concerning the containment of squares of paths and squares of cycles of arbitrary specified lengths and settles a conjecture of theirs in the affirmative. </p> <p><b>Monday 7.2.2022 at 10:00 <a href="http://www.ustavinformatiky.cz/">ICS</a>, room 419, <a href="https://kam.mff.cuni.cz/~tyomkyn/">Mykhaylo Tyomkyn</a> (Charles University): Limiting constants for weak saturation of hypergraphs</b></p> <p><u>Abstract</u>: For two r-uniform hypergraphs G and H we say that G is weakly H-saturated if the missing edges in G can be filled one by one, creating a new copy of H at every step. The quantity wsat(n,H) measures the smallest size of a weakly H-saturated r-graph of order n. For r=2 a short argument due to Alon (1985) shows that for any graph H, wsat(n,H)/n tends to a limit as n increases. Tuza conjectured in 1992 that for arbitrary r the quantity wsat(n,H)/n^{r-1} similarly has a limit c(H). I will present a recent proof of Tuza's conjecture.</p> <p>Joint work with Asaf Shapira (Tel Aviv University).</p> <h2>Past Seminars</h2> <p><b>Wednesday 12.1.2022 at 10:00 <a href="http://www.ustavinformatiky.cz/">ICS</a>, room 318, <a href="https://homepages.warwick.ac.uk/staff/Jan.Grebik/">Jan Greb&iacute;k</a> (Warwick): Local problems on bounded degree graphs</b></p> <table width="100%" border="0"> <tr> <td width="25%" height="220" align="center"> <img src="seminar-pictures/Grebik2022.jpg" width="300" class="fltrt"/> </td> <td width="75%"><p><strong></strong></p> <p><u>Abstract</u>: I will discuss some recent progress on connections between distributed computing and descriptive combinatorics. The connection is phrased in the language of local problems, i.e., coloring problems where a correctness of a given candidate coloring can be checked locally. In both fields, the goal is to understand how difficult is to produce a coloring that solves a given local problem. I will focus on the case of oriented paths, however, if time permits we might discuss other classes of graphs. This is joint work Vasek Rozhon.</p> </td> </tr> </table> <hr> <h2><a href="seminar2021.html">seminars in 2021</a></h2> <h2><a href="seminar2020.html">seminars in 2020</a></h2> <h2><a href="seminar2019.html">seminars in 2019</a></h2> <h2><a href="seminar2018.html">seminars in 2018</a></h2> <h2><a href="seminar2017.html">seminars in 2017</a></h2> <h2><a href="seminar2016.html">seminars in 2016</a></h2> </BODY> </HTML>