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Alon–Tarsi Number and Modulo Alon–Tarsi Number of Signed Graphs
We extend the concept of the Alon–Tarsi number for unsigned graph to signed one. Moreover, we introduce the modulo Alon–Tarsi number for a prime number p . We show that both the Alon–Tarsi number and modulo Alon–Tarsi number of a signed planar graph ( G , σ ) are at most 5, where the former result g...
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Published in: | Graphs and combinatorics 2019-09, Vol.35 (5), p.1051-1064 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We extend the concept of the Alon–Tarsi number for unsigned graph to signed one. Moreover, we introduce the modulo Alon–Tarsi number for a prime number
p
. We show that both the Alon–Tarsi number and modulo Alon–Tarsi number of a signed planar graph
(
G
,
σ
)
are at most 5, where the former result generalizes Zhu’s result for unsigned case and the latter one implies that
(
G
,
σ
)
is
Z
5
-colorable. |
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ISSN: | 0911-0119 1435-5914 |
DOI: | 10.1007/s00373-019-02056-9 |