Geodesic
A categorification for the signed chromatic polynomial
Zhiyun Cheng1 ; Ziyi Lei1 ; Yitian Wang1 ; Yanguo Zhang1
1Beijing Normal University
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which categorifies the signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.
DOI : 10.37236/10939
Classification : 05C31, 05C15, 05C22
Mots-clés : signed graph, graded cohomology groups

Zhiyun Cheng  1   ; Ziyi Lei  1   ; Yitian Wang  1   ; Yanguo Zhang  1

1 Beijing Normal University 
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     title = {A categorification for the signed chromatic polynomial},
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Zhiyun Cheng; Ziyi Lei; Yitian Wang; Yanguo Zhang. A categorification for the signed chromatic polynomial. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10939

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