Degree condition for completely independent spanning trees

Hong, Xiaochun; Liu, Qinghai

doi:10.1016/j.ipl.2016.05.004

Cited by 31 publications

(8 citation statements)

References 7 publications

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“…These conditions are based on the sufficient conditions for hamiltonicity: Dirac's condition [25] and Ore's condition [26]. The Dirac's condition has been generalized to more than two trees [27]- [29] and has been independently improved [28], [29] for two trees. Also, a recent paper has studied the problem on an interesting class of graphs: the class of k-trees, for which the authors have proven that there exist at least k/2 completely independent spanning trees [30].…”

Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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Abstract-We investigate the problem of computing Completely Independent Spanning Trees (CIST) under a practical approach. We aim to show that despite CISTs are very challenging to exhibit in some networks, they present a real interest in ad-hoc networks and can be computed to enhance the network robustness. We propose an original ILP formulation for CISTs and we show through simulation results on representative network models that several CISTs can be computed when the network density is sufficiently high. These results tend to reinforce the interest of CISTs for various network operations such as robustness, load-balancing, traffic splitting, . . . As an important point, our results show that both the density and the number of nodes have an impact on the number of CISTs that can be found on ad-hoc networks.

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Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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“…1010 (11) 1101( 14) 1110 (15) 1011 (12) 1001( 10) 0011( 4) 1000 (9) 1111 (16) 1111 (16) 1011 (12) 1101( 14) 0000( 1) 0111( 8) 0101( 6) 1000( 9) 0011( 4) 1100( 13) 0100( 5) 0001( 2) 0010 (3) 1110 (15) 1001 (10) 0110( 7) 1010( 11) 0110( 7) 0001( 2) 0100( 5) 0111 (8) 1110 (15) 1001( 10) 1111( 16) 1100( 13) 1000( 9) 1011( 12) 1101( 14) 0101( 6) 0010( 3) 0000( 1) 0011( 4) 1010 (11) Fig. 3.…”

Section: Lemma 32 ([15]unclassified

“…, 00001(2), 00010(3), 00011(4), 00100(5), 00101 (6), 00110 (7), 00111 (8), 01000 (9), 01001 (10), 01010 (11), 01011 (12), 01100 (13), 01101 (14), 01110 (15), 01111 (16), 10000 (17), 10001 (18), 10010 (19) 18) 11000( 25) 10000( 17) 00000 (1) 01111( 16) 01100( 13) 01101( 14) 01110( 15) 00010( 3) 00001( 2) 00100( 5) 10100( 21) 11011( 28) 00011( 4) 01011( 12) 00110( 7) 00101( 6) 00111( 8) 01001( 10 18) 00110( 7) 10100( 21) 10000 (17) 10011( 20) 11011( 28) 01001 (10) 01110( 15) 01000( 9) 01010( 11) 00001( 2) 00101( 6) 00010( 3) 00011( 4) 01011( 12) 01100( 13) 00000( 1) 11100( 29) 00111( 8) 00100…”

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Construction of Four Completely Independent Spanning Trees on Augmented Cubes

Mane¹,

Kandekar²,

Waphare³

2017

Preprint

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Let T1, T2, ......., T k be spanning trees in a graph G. If for any pair of vertices {u, v} of G, the paths between u and v in every Ti( 1 ≤ i ≤ k) do not contain common edges and common vertices, except the vertices u and v, then T1, T2, ......., T k are called completely independent spanning trees in G. The n−dimensional augmented cube, denoted as AQn, a variation of the hypercube possesses several embeddable properties that the hypercube and its variations do not possess. For AQn (n ≥ 6), construction of 4 completely independent spanning trees of which two trees with diameters 2n − 5 and two trees with diameters 2n − 3 are given.

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“…Péterfalvi [24] showed that, for any k 2, there exists k-connected graph which does not possess two CISTs. Accordingly, researches investigating sufficient conditions for graphs that admit multiple CISTs, such as degree-based conditions, can be found in [1], [3], [7], [15], [17]. Also, with the help of constructions, it has been confirmed that certain classes of graphs possess two CISTs, e.g., 4-connected maximal planar graphs [13], Cartesian product of any 2-connected graphs [14], 4-regular chordal rings [2], [23], crossed cubes [5], and several hypercube-variant networks [21].…”

Section: Introductionmentioning

confidence: 99%

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

Yang

Pai

Chang

et al. 2019

IEICE Trans. Inf. & Syst.

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A set of spanning trees of a graphs G are called completely independent spanning trees (CISTs for short) if for every pair of vertices x, y ∈ V(G), the paths joining x and y in any two trees have neither vertex nor edge in common, except x and y. Constructing CISTs has applications on interconnection networks such as fault-tolerant routing and secure message transmission. In this paper, we investigate the problem of constructing two CISTs in the balanced hypercube BH n , which is a hypercube-variant network and is superior to hypercube due to having a smaller diameter. As a result, the diameter of CISTs we constructed equals to 9 for BH 2 and 6n − 2 for BH n when n 3. key words: interconnection networks, completely independent spanning trees, balanced hypercubes, diameter

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Degree condition for completely independent spanning trees

Cited by 31 publications

References 7 publications

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Construction of Four Completely Independent Spanning Trees on Augmented Cubes

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

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