NDLI: On the Facial Thue Choice Number of Plane Graphs Via Entropy Compression Method

Content Provider	Springer Nature Link
Author	Škrabul’áková, Erika Przybyło, Jakub Schreyer, Jens
Copyright Year	2015
Abstract	Let G be a plane graph. A vertex-colouring $$\varphi $$ of G is called facial non-repetitive if for no sequence $$r_1 r_2 \ldots r_{2n}$$ , $$n\ge 1$$ , of consecutive vertex colours of any facial path it holds $$r_i=r_{n+i}$$ for all $$i=1,2,\ldots ,n$$ . A plane graph G is facial non-repetitively k -choosable if for every list assignment $$L:V\rightarrow 2^{\mathbb {N}}$$ with minimum list size at least k there is a facial non-repetitive vertex-colouring $$\varphi $$ with colours from the associated lists. The facial Thue choice number, $$\pi _{fl}(G)$$ , of a plane graph G is the minimum number k such that G is facial non-repetitively k-choosable. We use the so-called entropy compression method to show that $$\pi _{fl} (G)\le c \varDelta $$ for some absolute constant c and G a plane graph with maximum degree $$\varDelta $$ . Moreover, we give some better (constant) upper bounds on $$\pi _{fl} (G)$$ for special classes of plane graphs.
Ending Page	1153
Page Count	17
Starting Page	1137
File Format	PDF
ISSN	09110119
e-ISSN	14355914
Journal	Graphs and Combinatorics
Issue Number	3
Volume Number	32
Language	English
Publisher	Springer Japan
Publisher Date	2015-11-06
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Planar graphs; geometric and topological aspects of graph theory Non-repetitive sequence List vertex-colouring Engineering Design Combinatorics Facial non-repetitive colouring Plane graph Facial Thue choice number Entropy compression method
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science

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On the Facial Thue Choice Number of Plane Graphs Via Entropy Compression Method

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