Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, June 9, 2020.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
       May 2020              June 2020              July 2020      
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                 1  2       1  2  3  4  5  6             1  2  3  4
  3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
 10 11 12 13 14 15 16   14 15 16 17 18 19 20   12 13 14 15 16 17 18
 17 18 19 20 21 22 23   21 22 23 24 25 26 27   19 20 21 22 23 24 25
 24 25 26 27 28 29 30   28 29 30               26 27 28 29 30 31   
 31                                                                

Tuesday, June 9, 2020

2:00 pm in Zoom,Tuesday, June 9, 2020

Packing $(1,1,2,4)$-coloring of subcubic outerplanar graphs

Xujun Liu (University of Illinois, Urbana-Champaign)

Abstract: For $1\leq s_1 \le s_2 \le \ldots \le s_k$ and a graph $G$, a packing $(s_1, s_2, \ldots, s_k)$-coloring of $G$, is a partition of $V(G)$ into sets $V_1, V_2, \ldots, V_k$ such that for each $1\leq i \leq k$ the distance between any two distinct $x,y\in V_i$ is at least $s_i + 1$. The packing chromatic number, $\chi_p(G)$, of a graph $G$ is the smallest $k$ such that $G$ has a packing $(1,2, \ldots, k)$-coloring. It is known that there are trees of maximum degree 4 and subcubic graphs $G$ with arbitrarily large $\chi_p(G)$. Recently, there was a series of papers on packing $(s_1, s_2, \ldots, s_k)$-colorings of subcubic graphs in various classes. We show that every $2$-connected subcubic outerplanar graph has a packing $(1,1,2)$-coloring and every subcubic outerplanar graph is packing $(1,1,2,4)$-colorable. Our results are sharp in the sense that there are $2$-connected subcubic outerplanar graphs that are not packing $(1,1,3)$-colorable and there are subcubic outerplanar graphs that are not packing $(1,1,2,5)$-colorable. This is joint work with Alexandr Kostochka.

Please contact Sean English at SEnglish@illinois.edu for the Zoom information.