Sudoku number of graphs
نویسندگان
چکیده
We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let G=(V,E) be of order n with chromatic number χ(G)=k and let S⊆V. C0 k-coloring induced subgraph G[S]. The is called an extendable if can extended to G. say that G uniquely smallest such G[S] which admits denoted sn(G). In this paper we initiate study parameter. first show parameter related list graphs. Section 2, basic properties are color dominating vertices, numbers degree given. Particularly, obtained necessary conditions for being extendable, coloring. 3, determined various families showed connected has sn(G) = 1 only bipartite. Consequently, every tree T sn(T) 1. also proved sn(G)=|V(G)|−1 Kn. Moreover, small may have arbitrarily large number. 4, partial problem NP-complete. Extendable nice tools providing
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2023
ISSN: ['2543-3474', '0972-8600']
DOI: https://doi.org/10.1080/09728600.2023.2218917