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SUMMARY:Vahan Mkrtchyan (Boston College)
DTSTART:20220910T140000Z
DTEND:20220910T150000Z
DTSTAMP:20260423T021227Z
UID:YMC/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YMC/40/">Nor
 mal edge-colorings of cubic graphs</a>\nby Vahan Mkrtchyan (Boston College
 ) as part of Yerevan Mathematical Colloquium\n\n\nAbstract\nIf $G$ is a cu
 bic graph and $f:E(G)\\rightarrow \\{1\,...\,k\\}$ is a proper $k$-edge-co
 loring\, then an edge $e=uv$ of $G$ is called poor (or rich) with respect 
 to $f$\, if $u$ and $v$ together are incident to exactly $3$ (or $5$) colo
 rs in $f$. A proper $k$-edge-coloring is called normal in $G$\, if all edg
 es of $G$ are poor or rich with respect to this coloring. The Petersen col
 oring of Jaeger states that all bridgeless cubic graphs admit a normal edg
 e-coloring with at most $5$ colors. If a cubic graph contains a bridge\, t
 hen it was known previously that all such cubic graphs admit a normal edge
 -coloring with at most $9$ colors. In this talk\, we will show that all cu
 bic graphs admit a normal edge-coloring using at most $7$ colors. This bou
 nd is best-possible\, in a sense that it is tight for infinitely many cubi
 c graphs. This is a joint work with Giuseppe Mazzuoccolo.\n\ntalk host: Pe
 tros Petrosyan (YSU)\n
LOCATION:https://researchseminars.org/talk/YMC/40/
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