Independence, irredundance, degrees and chromatic number in graphs
نویسندگان
چکیده
Let (G) and IR(G) denote the independence number and the upper irredundance number of a graph G. We prove that in any graph of order n, minimum degree and maximum degree =0, IR(G)6 n=(1 + = ) and IR(G) − (G)6 (( − 2)=2 )n. The two bounds are attained by arbitrarily large graphs. The second one proves a conjecture by Rautenbach related to the case = 3. When the chromatic number of G is less than , it can be improved to IR(G)− (G)6 (( − 2)=2 )n in any non-empty graph of order n¿ 2. c © 2002 Elsevier Science B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 259 شماره
صفحات -
تاریخ انتشار 2002