Star number and star arboricity of a complete multigraph |
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Authors: | Chiang Lin Tay-Woei Shyu |
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Institution: | (1) Department of Mathematics, National Central University, Chung-Li, Taiwan;(2) College of International Studies and Education for Overseas Chinese, National Taiwan Normal University, Linkou, Taipei Hsien, Taiwan |
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Abstract: | Let G be a multigraph. The star number s(G) of G is the minimum number of stars needed to decompose the edges of G. The star arboricity sa(G) of G is the minimum number of star forests needed to decompose the edges of G. As usual λK
n
denote the λ-fold complete graph on n vertices (i.e., the multigraph on n vertices such that there are λ edges between every pair of vertices). In this paper, we prove that for n ⩾ 2
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Keywords: | decomposition star arboricity star forest complete multigraph |
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