On $$\alpha $$-Vertex Choosability of Graphs
| Autor: | K. Augusthy Germina, P. Soorya, Sudev Naduvath |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0106 biological sciences
Physics Combinatorics Choice number Vertex (graph theory) Simple graph 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 02 engineering and technology 01 natural sciences Engineering (miscellaneous) 010606 plant biology & botany |
| Zdroj: | National Academy Science Letters. 44:343-346 |
| ISSN: | 2250-1754 0250-541X |
| DOI: | 10.1007/s40009-020-01006-x |
| Popis: | A connected, simple graph G with vertex set $$V(G)=\{1,2,\ldots ,n\}$$ is said to be vertex (n, k)-choosable, if there exists a collection of subsets $$\left\{ S_k(v)\subseteq V(G): v\in V\right\} $$ of cardinality k, such that $$S_k(u)\cap S_k(v)=\emptyset $$ for all $$uv\in E(G)$$ , where k is a positive integer less than n. The maximum value of such k is called the vertex choice number of G. In this paper, we introduce the notion of $$\alpha $$ - choosability of graphs in terms of their vertex (n, k)-choice number and initiate a study on the structural characteristics of $$\alpha $$ -choosable graphs. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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