On the existence of 5-sun systems

Fu, Chin-Mei; Huang, Ming-Hway; Lin, Ya-Ju

doi:10.1016/j.disc.2013.09.007

Cited by 10 publications

(30 citation statements)

References 16 publications

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“…As far as we know, this problem has been completely settled only when k = 3, 5 [8,10], k = 4, 6, 8 [12], and when k = 10, 14 or 2 4 t ≥ [9]. It is important to notice that, as a consequence of a general result proved in [14], condition (*) is sufficient whenever v is large enough with respect to k. These results seem to suggest the following.…”

Section: Introductionmentioning

confidence: 90%

“…Proof The existence of 3‐sun systems and 5‐sun systems has been solved in [10] and in [8], respectively. Hence we can suppose

k \geq 7

and

2 k < v < 6 k

.…”

Section: It Is Sufficient To Solve 2kmentioning

confidence: 99%

“…Since the existence of

p

‐sun systems with

p = 3, 5

has been proved in [10] and in [8], respectively, here we can assume

p \geq 7

.…”

Section: Construction Of P‐sun Systems P Primementioning

confidence: 99%

“…In this paper we study the existence problem for

k

‐sun systems of

K_{v}

(

v > 1

). Clearly, for such a system to exist we must have

v \geq 2 k and v (v - 1) \equiv 0 (\mod 4 k) . (*)

As far as we know, this problem has been completely settled only when

k = 3, 5

[8,10],

k = 4, 6, 8

[12], and when

k = 10, 14

2^{t} \geq 4

[9]. It is important to notice that, as a consequence of a general result proved in [14], condition (*) is sufficient whenever

v

is large enough with respect to

k

.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A reduction of the spectrum problem for odd sun systems and the prime case

Buratti

Pasotti

Traetta

2020

J of Combinatorial Designs

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show abstract

Section: Introductionmentioning

confidence: 90%

“…Proof The existence of 3‐sun systems and 5‐sun systems has been solved in [10] and in [8], respectively. Hence we can suppose

k \geq 7

and

2 k < v < 6 k

.…”

Section: It Is Sufficient To Solve 2kmentioning

confidence: 99%

“…Since the existence of

p

‐sun systems with

p = 3, 5

has been proved in [10] and in [8], respectively, here we can assume

p \geq 7

.…”

Section: Construction Of P‐sun Systems P Primementioning

confidence: 99%

“…In this paper we study the existence problem for

k

‐sun systems of

K_{v}

(

v > 1

). Clearly, for such a system to exist we must have

v \geq 2 k and v (v - 1) \equiv 0 (\mod 4 k) . (*)

As far as we know, this problem has been completely settled only when

k = 3, 5

[8,10],

k = 4, 6, 8

[12], and when

k = 10, 14

2^{t} \geq 4

[9]. It is important to notice that, as a consequence of a general result proved in [14], condition (*) is sufficient whenever

v

is large enough with respect to

k

.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A reduction of the spectrum problem for odd sun systems and the prime case

Buratti

Pasotti

Traetta

2020

J of Combinatorial Designs

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show abstract

“…Liang and Guo [10,11] gave the existence spectrum of a k-sun system of order v as k = 3, 4, 5, 6, 8 by using a recursive construction. Recently, Fu et al [6] investigate the problem of the decomposition of complete tripartite graphs into 3-suns and find the necessary and sufficient condition for the existence of a k-sun system of order v in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Decompositions of balanced complete bipartite graphs into suns and stars

Jou¹,

Lin²

2018

ijcms

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Let L = {H 1 , H 2 ,. .. , H r } be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer α i copies of H i , where i ∈ {1, 2,. .. , r}. Let S(C k/2) and S k denote a sun and a star with k edges, respectively. In this paper, we prove that a balanced complete bipartite graph with 2n vertices has a {S(C k/2), S k }-decomposition if and only if 8 ≤ k ≤ n, k ≡ 0 (mod 4) and n 2 ≡ 0 (mod k).

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Decomposing certain equipartite graphs into t-fold bristled graphs

Kandan

2019

Recent Trends in Pure and Applied Mathematics

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On the existence of 5-sun systems

Cited by 10 publications

References 16 publications

A reduction of the spectrum problem for odd sun systems and the prime case

A reduction of the spectrum problem for odd sun systems and the prime case

Decompositions of balanced complete bipartite graphs into suns and stars

Decomposing certain equipartite graphs into t-fold bristled graphs

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