Sufficient conditions for Hamilton-connected graphs in terms of (signless Laplacian) spectral radius

Zhou, Qing; Wang, Ligong; Lu, Yilong

doi:10.1016/j.laa.2020.02.022

Cited by 5 publications

(4 citation statements)

References 26 publications

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“…In 2020, Zhou, Wang and Lu [198] provided a further improvement on Theorems 4.22, 4.23 and 4.24. More precisely, they proved that if n ≥ 11 and G satisfies δ(G) ≥ 3 and e(G) ≥ n−3 2 + 13, then G is Hamilton-connected unless G belongs to some exceptions.…”

Section: Problem For K-connectivitymentioning

confidence: 99%

“…More precisely, they proved that if n ≥ 11 and G satisfies δ(G) ≥ 3 and e(G) ≥ n−3 2 + 13, then G is Hamilton-connected unless G belongs to some exceptions. Theorem 4.25 (Zhou-Wang-Lu [198]). Let G be a connected graph on n ≥ 14 vertices with minimum degree δ…”

Section: Problem For K-connectivitymentioning

confidence: 99%

“…Theorem 4.26 (Zhou-Wang-Lu [198]). Let G be a connected graph on n ≥ 13 vertices with minimum degree δ ≥ 3.…”

Section: Problem For K-connectivitymentioning

confidence: 99%

See 2 more Smart Citations

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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This survey is two-fold. We first report new progress on the spectral extremal results on the Turán type problems in graph theory. More precisely, we shall summarize the spectral Turán function in terms of the adjacency spectral radius and the signless Laplacian spectral radius for various graphs. For instance, the complete graphs, general graphs with chromatic number at least three, complete bipartite graphs, odd cycles, even cycles, color-critical graphs and intersecting triangles.The second goal is to conclude some recent results of the spectral conditions on some graphical properties. By a unified method, we present some sufficient conditions based on the adjacency spectral radius and the signless Laplacian spectral radius for a graph to be Hamiltonian, k-Hamiltonian, k-edge-Hamiltonian, traceable, k-pathcoverable, k-connected, k-edge-connected, Hamilton-connected, perfect matching and β-deficient.

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Section: Problem For K-connectivitymentioning

confidence: 99%

Section: Problem For K-connectivitymentioning

confidence: 99%

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A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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“…As a special case of k-leaf-connectedness, there are many sufficient conditions to assure a graph to be 2-leaf-connected (see for example [14,[16][17][18]). By introducing the minimum degree δ as a new parameter, Chen and Zhang [5] presented a sufficient condition for a graph with δ ≥ t ≥ 2 to be Hamilton-connected: e(G)…”

Section: Introductionmentioning

confidence: 99%

An improvement of sufficient condition for $k$-leaf-connected graphs

Ma¹,

Ao²,

Liu³

et al. 2022

Preprint

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and given any subset S ⊆ V(G) with |S | = k, G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if and only if it is Hamilton-connected. In this paper, we present a best possible condition based upon the size to guarantee a graph to be k-leaf-connected, which not only improves the results of Gurgel and Wakabayashi [On k-leaf-connected graphs, J. Combin. Theory Ser. B 41 (1986) 1-16] and Ao, Liu, Yuan and Li [Improved sufficient conditions for k-leafconnected graphs, Discrete Appl. Math. 314 (2022) 17-30], but also extends the result of Xu, Zhai and Wang [An improvement of spectral conditions for Hamilton-connected graphs, Linear Multilinear Algebra, 2021]. Our key approach is showing that an (n+k−1)closed non-k-leaf-connected graph must contain a large clique if its size is large enough. As applications, sufficient conditions for a graph to be k-leaf-connected in terms of the (signless Laplacian) spectral radius of G or its complement are also presented.

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