On the number of solutions in random graph $k$-colouring
Let $k \ge 3$ be a fixed integer. We exactly determine the asymptotic distribution of $\ln Z_k(G(n,m))$, where $Z_k(G(n,m))$ is the number of $k$-colourings of the random graph $G(n,m)$. A crucial observation to this aim is that the fluctuations in the number of colourings can be attributed to the f...
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| creator | Rassmann, Felicia |
| description | Let $k \ge 3$ be a fixed integer. We exactly determine the asymptotic
distribution of $\ln Z_k(G(n,m))$, where $Z_k(G(n,m))$ is the number of
$k$-colourings of the random graph $G(n,m)$. A crucial observation to this aim
is that the fluctuations in the number of colourings can be attributed to the
fluctuations in the number of small cycles in $G(n,m)$. Our result holds for a
wide range of average degrees, and for $k$ exceeding a certain constant $k_0$
it covers all average degrees up to the so-called "condensation phase
transition". |
| doi_str_mv | 10.48550/arxiv.1609.04191 |
| format | Article |
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distribution of $\ln Z_k(G(n,m))$, where $Z_k(G(n,m))$ is the number of
$k$-colourings of the random graph $G(n,m)$. A crucial observation to this aim
is that the fluctuations in the number of colourings can be attributed to the
fluctuations in the number of small cycles in $G(n,m)$. Our result holds for a
wide range of average degrees, and for $k$ exceeding a certain constant $k_0$
it covers all average degrees up to the so-called "condensation phase
transition".</description><identifier>DOI: 10.48550/arxiv.1609.04191</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2016-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1609.04191$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1609.04191$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Rassmann, Felicia</creatorcontrib><title>On the number of solutions in random graph $k$-colouring</title><description>Let $k \ge 3$ be a fixed integer. We exactly determine the asymptotic
distribution of $\ln Z_k(G(n,m))$, where $Z_k(G(n,m))$ is the number of
$k$-colourings of the random graph $G(n,m)$. A crucial observation to this aim
is that the fluctuations in the number of colourings can be attributed to the
fluctuations in the number of small cycles in $G(n,m)$. Our result holds for a
wide range of average degrees, and for $k$ exceeding a certain constant $k_0$
it covers all average degrees up to the so-called "condensation phase
transition".</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjz1PwzAUAL0woMIPYKqHrgnPieP4jajiS6rUpXv04vi1FoldOQ2Cf48oTLed7oR4UFBq2zTwSPkrfJbKAJagFapbYfdRXk5exmXqfZaJ5ZzG5RJSnGWIMlMc0iSPmc4nufnYFC6NackhHu_EDdM4-_t_rsTh5fmwfSt2-9f37dOuINOqonLIzihnNGgArtFSwy067rE2iEC9R9OT0wMP1g8Vq9YYJmisqzwx1yux_tNe07tzDhPl7-53obsu1D9acUEr</recordid><startdate>20160914</startdate><enddate>20160914</enddate><creator>Rassmann, Felicia</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160914</creationdate><title>On the number of solutions in random graph $k$-colouring</title><author>Rassmann, Felicia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-2c9fc61c640400f398a5f79cfb936990abe96bac4dfd8ed2f1766fa058c2eaff3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Rassmann, Felicia</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Rassmann, Felicia</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the number of solutions in random graph $k$-colouring</atitle><date>2016-09-14</date><risdate>2016</risdate><abstract>Let $k \ge 3$ be a fixed integer. We exactly determine the asymptotic
distribution of $\ln Z_k(G(n,m))$, where $Z_k(G(n,m))$ is the number of
$k$-colourings of the random graph $G(n,m)$. A crucial observation to this aim
is that the fluctuations in the number of colourings can be attributed to the
fluctuations in the number of small cycles in $G(n,m)$. Our result holds for a
wide range of average degrees, and for $k$ exceeding a certain constant $k_0$
it covers all average degrees up to the so-called "condensation phase
transition".</abstract><doi>10.48550/arxiv.1609.04191</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | On the number of solutions in random graph $k$-colouring |
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