𝔖 Bobbio Scriptorium
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Improper Choosability and Property B

✍ Scribed by Ross J. Kang

Book ID
112121141
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
540 KB
Volume
73
Category
Article
ISSN
0364-9024

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📜 SIMILAR VOLUMES

Improper choosability of graphs and maxi
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## Abstract Improper choosability of planar graphs has been widely studied. In particular, Škrekovski investigated the smallest integer __g__~k~ such that every planar graph of girth at least __g__~k~ is __k__‐improper 2‐choosable. He proved [9] that 6 ≤ __g__~1~ ≤ 9; 5 ≤  __g__~2~ ≤ 7; 5 ≤ __g__~3

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It is proved that the choice number of every graph G embedded on a surface of Euler genus ε ≥ 1 and ε = 3 is at most the Heawood number H(ε) = (7 + √ 24ε + 1)/2 and that the equality holds if and only if G contains the complete graph K H(ε) as a subgraph.