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SUMMARY:Chun-Hung Liu (Texas A&M University)
DTSTART:20201119T020000Z
DTEND:20201119T030000Z
DTSTAMP:20260423T021016Z
UID:SCMSComb/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/23/
 ">Clustered coloring for Hadwiger type problems</a>\nby Chun-Hung Liu (Tex
 as A&M University) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nHa
 dwiger (Hajos and Gerards and Seymour\, respectively) conjectured that \nt
 he vertices of  every graph with no $K_{t+1}$ minor (topological minor \na
 nd odd minor\, respectively) can be  colored with t colors such that any \
 npair of adjacent vertices receive different colors. These conjectures \na
 re stronger than the Four Color Theorem and are either open or false  \nin
  general. A weakening of these conjectures is to consider clustered \ncolo
 ring which only requires every monochromatic component to have \nbounded s
 ize instead of size 1. It is known that t colors are still \nnecessary for
  the clustered coloring version of those three conjectures. \nJoint with D
 avid Wood\, we prove a series of tight results about \nclustered coloring 
 on graphs with no subgraph isomorphic to a fixed \ncomplete bipartite grap
 h. These results have a number of applications. \nIn particular\, they imp
 ly that the clustered coloring version of Hajos’ \nconjecture is true fo
 r bounded treewidth graphs in a stronger sense: \n$K_{t+1}$ topological mi
 nor free graphs of bounded treewidth are clustered \nt-list-colorable. The
 y also lead to the first linear upper bound for the \nclustered coloring v
 ersion of Hajos’ conjecture and the currently best \nupper bound for the
  clustered coloring version of the Gerards-Seymour \nconjecture.\n\npw 030
 332\n
LOCATION:https://researchseminars.org/talk/SCMSComb/23/
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