A Necessary and Sufficient Condition for the Star Decomposition of Complete Graphs

Chiang Lin; Tay Woei Shyu

doi:10.1002/(SICI)1097-0118(199612)23:4<361::AID-JGT5>3.0.CO;2-P

A Necessary and Sufficient Condition for the Star Decomposition of Complete Graphs

Chiang Lin^*, Tay Woei Shyu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

In this paper we prove the following result. Let m₁ ≥ m₂ ≥ ⋯ ≥ m_l be nonnegative integers. A necessary and sufficient condition for the complete graph K_n to be decomposed into stars S_m1, S_m2, . . . , S_ml is ∑^k_i=1 m_i ≤ ∑^k_i=1 (n - i) for k = 1, 2, . . . , n - 1 and ∑^l_i=1 m_i = (ⁿ₂).

Original language	English
Pages (from-to)	361-364
Number of pages	4
Journal	Journal of Graph Theory
Volume	23
Issue number	4
DOIs	https://doi.org/10.1002/(SICI)1097-0118(199612)23:4<361::AID-JGT5>3.0.CO;2-P
Publication status	Published - 1996 Dec
Externally published	Yes

ASJC Scopus subject areas

Geometry and Topology

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10.1002/(SICI)1097-0118(199612)23:4<361::AID-JGT5>3.0.CO;2-P

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abstract = "In this paper we prove the following result. Let m1 ≥ m2 ≥ ⋯ ≥ ml be nonnegative integers. A necessary and sufficient condition for the complete graph Kn to be decomposed into stars Sm1, Sm2, . . . , Sml is ∑ki=1 mi ≤ ∑ki=1 (n - i) for k = 1, 2, . . . , n - 1 and ∑li=1 mi = (n2).",

author = "Chiang Lin and Shyu, {Tay Woei}",

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AU - Shyu, Tay Woei

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N2 - In this paper we prove the following result. Let m1 ≥ m2 ≥ ⋯ ≥ ml be nonnegative integers. A necessary and sufficient condition for the complete graph Kn to be decomposed into stars Sm1, Sm2, . . . , Sml is ∑ki=1 mi ≤ ∑ki=1 (n - i) for k = 1, 2, . . . , n - 1 and ∑li=1 mi = (n2).

AB - In this paper we prove the following result. Let m1 ≥ m2 ≥ ⋯ ≥ ml be nonnegative integers. A necessary and sufficient condition for the complete graph Kn to be decomposed into stars Sm1, Sm2, . . . , Sml is ∑ki=1 mi ≤ ∑ki=1 (n - i) for k = 1, 2, . . . , n - 1 and ∑li=1 mi = (n2).

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A Necessary and Sufficient Condition for the Star Decomposition of Complete Graphs

Abstract

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