Geodesic
On the location of chromatic zeros of series-parallel graphs
Ferenc Bencs1 ; Jeroen Huijben1 ; Guus Regts1
1University of Amsterdam
The electronic journal of combinatorics, Tome 30 (2023) no. 3
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In this paper we consider the zeros of the chromatic polynomial of series-parallel graphs. Complementing a result of Sokal, giving density outside the disk $|q-1|\leq1$, we show density of these zeros in the half plane $\Re(q)>3/2$ and we show there exists an open region $U$ containing the interval $(0,32/27)$ such that $U\setminus\{1\}$ does not contain zeros of the chromatic polynomial of series-parallel graphs. We also disprove a conjecture of Sokal by showing that for each large enough integer $\Delta$ there exists a series-parallel graph for which all vertices but one have degree at most $\Delta$ and whose chromatic polynomial has a zero with real part exceeding $\Delta$.
DOI : 10.37236/11204
Classification : 05C31, 05C15, 30D45
Mots-clés : chromatic polynomial, generalized theta graphs

Ferenc Bencs  1   ; Jeroen Huijben  1   ; Guus Regts  1

1 University of Amsterdam 
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     title = {On the location of chromatic zeros of series-parallel graphs},
     journal = {The electronic journal of combinatorics},
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Ferenc Bencs; Jeroen Huijben; Guus Regts. On the location of chromatic zeros of series-parallel graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11204

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