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学者姓名：洪艳梅
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Abstract ：
Mader proved that, for any tree T of order m $m$, every k -connected graph G with delta( G ) >= 2 (k + m - 1 )( 2) + m - 1 contains a subtree T ' congruent to T such that G - V( T ' ) is k-connected. We proved that any graph G with minimum degree delta( G ) >= 2 k contains k-connected triples. As a corollary, we prove that, for any tree T of order m , every k -connected graph G with delta( G ) >= 3 k + 4 m - 6 contains a subtree T ' congruent to T such that G - V( T ' )-is still k -connected, improving Mader's condition to a linear bound.
Keyword ：
connectivity-keeping trees connectivity-keeping trees k-connected k-connected k-connected triples k-connected triples
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| GB/T 7714 | Liu, Qinghai , Ying, Kai , Hong, Yanmei . Highly connected triples and Mader's conjecture [J]. | JOURNAL OF GRAPH THEORY , 2024 . |
| MLA | Liu, Qinghai 等. "Highly connected triples and Mader's conjecture" . | JOURNAL OF GRAPH THEORY (2024) . |
| APA | Liu, Qinghai , Ying, Kai , Hong, Yanmei . Highly connected triples and Mader's conjecture . | JOURNAL OF GRAPH THEORY , 2024 . |
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Gallai's conjecture asserts that every connected graph of order n can be decomposed into inverted right perpendicularn/2inverted left perpendicular paths. A graph G is k -degenerated if each subgraph admits a vertex with degree no more than k . In this paper, we characterize the graphs that contain a path through specified edges. As a result, we prove that a connected 3-degenerated graph of order n that is not isomorphic to K-3 or K-5(-) can be decomposed into left perpendicularn/2right perpendicular paths, which extends three theorems of [2,3,12]. (c) 2024 Elsevier B.V. All rights reserved.
Keyword ：
3-degenerated 3-degenerated Gallai's conjecture Gallai's conjecture Path-decomposition Path-decomposition
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| GB/T 7714 | Zhang, Junhao , Liu, Qinghai , Hong, Yanmei . Gallai's conjecture for 3-degenerated graphs [J]. | DISCRETE MATHEMATICS , 2024 , 347 (7) . |
| MLA | Zhang, Junhao 等. "Gallai's conjecture for 3-degenerated graphs" . | DISCRETE MATHEMATICS 347 . 7 (2024) . |
| APA | Zhang, Junhao , Liu, Qinghai , Hong, Yanmei . Gallai's conjecture for 3-degenerated graphs . | DISCRETE MATHEMATICS , 2024 , 347 (7) . |
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Hasunuma conjectured that for any tree of order m and for any k-connected (resp. k-edge-connected) graph G, if delta(G)>= k+m-1 then G contains a subgraph H congruent to T such that G-E(H) is k-connected (resp. k-edge-connected). Hasunuma verified the conjecture for k=1,2. In this paper, we confirm the conjecture when k=3.
Keyword ：
Connectivity Connectivity Subdivision Subdivision Trees Trees
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| GB/T 7714 | Liu, Haiyang , Liu, Qinghai , Hong, Yanmei . Connectivity keeping trees in 3-connected or 3-edge-connected graphs [J]. | DISCRETE MATHEMATICS , 2023 , 346 (12) . |
| MLA | Liu, Haiyang 等. "Connectivity keeping trees in 3-connected or 3-edge-connected graphs" . | DISCRETE MATHEMATICS 346 . 12 (2023) . |
| APA | Liu, Haiyang , Liu, Qinghai , Hong, Yanmei . Connectivity keeping trees in 3-connected or 3-edge-connected graphs . | DISCRETE MATHEMATICS , 2023 , 346 (12) . |
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Mader conjectured that for any tree T $T$ of order m $m$, every k $k$-connected graph G $G$ with minimum degree at least L 3 k 2 RIGHT FLOOR + m - 1 $\lfloor \frac{3k}{2}\rfloor +m-1$ contains a subtree T ' approximately equal to T $T<^>{\prime} \cong T$ such that G - V ( T ' ) $G-V(T<^>{\prime} )$ is k $k$-connected. In this article, we give a characterization for a subgraph to contain an embedding of a specified tree avoiding some vertex. As a corollary, we confirm Mader's conjecture for k <= 3 $k\le 3$.
Keyword ：
connectivity connectivity embedding embedding tree tree
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| GB/T 7714 | Hong, Yanmei , Liu, Qinghai . Mader's conjecture for graphs with small connectivity [J]. | JOURNAL OF GRAPH THEORY , 2022 , 101 (3) : 379-388 . |
| MLA | Hong, Yanmei 等. "Mader's conjecture for graphs with small connectivity" . | JOURNAL OF GRAPH THEORY 101 . 3 (2022) : 379-388 . |
| APA | Hong, Yanmei , Liu, Qinghai . Mader's conjecture for graphs with small connectivity . | JOURNAL OF GRAPH THEORY , 2022 , 101 (3) , 379-388 . |
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Abstract ：
Mader (2010) conjectured that for any tree T of order m, every k-connected graph G with minimum degree at least [3k/2]+ m-1 contains a subtree T' congruent to T such that G-V(T') is k-connected. A caterpillar is a tree in which a single path is incident to every edge. The conjecture has been proved when k = 1 and for some special caterpillars when k = 2. A spider is a tree with at most one vertex with degree more than 2. In this paper, we confirm the conjecture for all caterpillars and spiders when k = 2. Spider (C) 2020 Elsevier B.V. All rights reserved.
Keyword ：
2-connected graphs 2-connected graphs Caterpillars Caterpillars Connectivity Connectivity Spider Spider Trees Trees
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| GB/T 7714 | Hong, Yanmei , Liu, Qinghai , Lu, Changhong et al. Connectivity keeping caterpillars and spiders in 2-connected graphs [J]. | DISCRETE MATHEMATICS , 2021 , 344 (3) . |
| MLA | Hong, Yanmei et al. "Connectivity keeping caterpillars and spiders in 2-connected graphs" . | DISCRETE MATHEMATICS 344 . 3 (2021) . |
| APA | Hong, Yanmei , Liu, Qinghai , Lu, Changhong , Ye, Qingjie . Connectivity keeping caterpillars and spiders in 2-connected graphs . | DISCRETE MATHEMATICS , 2021 , 344 (3) . |
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It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of disjoint cycles. In this paper, we show that the conjecture is true for connected claw-free cubic graphs, and, furthermore, any edge not contained any triangle appears only on the tree or on the matching. Then we show that the edge set of every connected cubic graph (except for K-4 and K-3,K-3) can be decomposed into a spanning tree and a family of disjoint paths of length at most 2. (C) 2020 Elsevier B.V. All rights reserved.
Keyword ：
Claw-free graph Claw-free graph Cubic graph Cubic graph Hoffmann-Ostenhof's conjecture Hoffmann-Ostenhof's conjecture
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| GB/T 7714 | Hong, Yanmei , Liu, Qinghai , Yu, Nannan . Edge decomposition of connected claw-free cubic graphs [J]. | DISCRETE APPLIED MATHEMATICS , 2020 , 284 : 246-250 . |
| MLA | Hong, Yanmei et al. "Edge decomposition of connected claw-free cubic graphs" . | DISCRETE APPLIED MATHEMATICS 284 (2020) : 246-250 . |
| APA | Hong, Yanmei , Liu, Qinghai , Yu, Nannan . Edge decomposition of connected claw-free cubic graphs . | DISCRETE APPLIED MATHEMATICS , 2020 , 284 , 246-250 . |
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For two digraphs D = (V-1 , A(1)) and H = (V-2, A(2)), the lexicographic product digraph D[H] is the digraph with vertex set V-1 x V-2. There is an arc from vertex (x(1), y(1)) to vertex (x(2), y(2)) in D[H] if and only if either x(1) x(2) is an element of A(1) or x(1) = x(2) and y(1)y(2) is an element of A(2). The minimum degree and the arc-connectivity of D are denoted by delta(D) and lambda(D), respectively. We prove that for any two digraphs D and H, lambda(D[H]) >= min{n(t + lambda(D) - delta(D) - 1) + delta(D[H]), n(2)lambda(D)} holds for any t <= min{delta (D) - lambda(D) +1, lambda(D) + 1, n - 1}, where n = vertical bar V (H)vertical bar. As a consequence, lambda(D[H]) >= n(lambda(D) - delta(D)) + delta(D[H]). We also provide some sufficient conditions for D[H] to have maximum reliability with respected the connectedness and super connectedness. (C) 2019 Elsevier Inc. All rights reserved.
Keyword ：
Arc-connectivity Arc-connectivity Interconnection networks Interconnection networks Lexicographic product digraph Lexicographic product digraph Reliability Reliability Super-arc-connected Super-arc-connected
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| GB/T 7714 | Liu, Qinghai , Hong, Yanmei . The reliability of lexicographic product digraphs [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2019 , 358 : 449-454 . |
| MLA | Liu, Qinghai et al. "The reliability of lexicographic product digraphs" . | APPLIED MATHEMATICS AND COMPUTATION 358 (2019) : 449-454 . |
| APA | Liu, Qinghai , Hong, Yanmei . The reliability of lexicographic product digraphs . | APPLIED MATHEMATICS AND COMPUTATION , 2019 , 358 , 449-454 . |
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The revised Szeged index of a graph is defined as Sz* (G) =Sigma(e=uv is an element of E)(n(u)(e) + n(0)(e)/2 (n(v)(e) + n(0)(e)/2) where n(u)(e) and n(v)(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n(0)(e) is the number of vertices equidistant to u and v. In the paper, we acquired the lower bound of revised Szeged index among all tricyclic graphs, and the extremal graphs that attain the lower bound are determined.
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| GB/T 7714 | Ji, Shengjin , Hong, Yanmei , Liu, Mengmeng et al. The Lower Bound of Revised Szeged Index with Respect to Tricyclic Graphs [J]. | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2018 , 79 (3) : 757-778 . |
| MLA | Ji, Shengjin et al. "The Lower Bound of Revised Szeged Index with Respect to Tricyclic Graphs" . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 79 . 3 (2018) : 757-778 . |
| APA | Ji, Shengjin , Hong, Yanmei , Liu, Mengmeng , Wang, Jianfeng . The Lower Bound of Revised Szeged Index with Respect to Tricyclic Graphs . | MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY , 2018 , 79 (3) , 757-778 . |
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The revised Szeged index of a graph is defined as Sz ∗(G) = Σe=uv∈E(nu(e) + n0(e)/2)(nv(e) + n0(e)/2), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n0(e) is the number of vertices equidistant to u and v. In the paper, we acquired the lower bound of revised Szeged index among all tricyclic graphs, and the extremal graphs that attain the lower bound are determined. © 2018 University of Kragujevac, Faculty of Science. All rights reserved.
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| GB/T 7714 | Ji, S. , Hong, Y. , Liu, M. et al. The lower bound of revised Szeged index with respect to tricyclic graphs [J]. | Match , 2018 , 79 (3) : 757-778 . |
| MLA | Ji, S. et al. "The lower bound of revised Szeged index with respect to tricyclic graphs" . | Match 79 . 3 (2018) : 757-778 . |
| APA | Ji, S. , Hong, Y. , Liu, M. , Wang, J. . The lower bound of revised Szeged index with respect to tricyclic graphs . | Match , 2018 , 79 (3) , 757-778 . |
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Let d = {(d(1)(+), d(1)(-)),..., (d(n)(+), d(n)(-))} be a sequence of of nonnegative integers pairs. If a digraph D with V `(D) = {v(1), v(2),..., v(n)} satisfies d(D)(+) (v(i)) = d(i)(+) and d(D)(-) (v(i)) = d(i)(-) for each i with 1 <= i <= n, then d is called a degree sequence of D. If D is a strict digraph, then d is called a strict digraphic sequence. Let < d > be the collection of digraphs with degree sequence d. We characterize strict digraphic sequences d for which there exists a strict strong digraph D epsilon < d >. (C) 2016 Wiley Periodicals, Inc.
Keyword ：
degree sequence degree sequence degree sequence realizations degree sequence realizations strongly connected strongly connected
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| GB/T 7714 | Hong, Yanmei , Liu, Qinghai , Lai, Hong-Jian . Characterization of Digraphic Sequences with Strongly Connected Realizations [J]. | JOURNAL OF GRAPH THEORY , 2017 , 84 (2) : 191-201 . |
| MLA | Hong, Yanmei et al. "Characterization of Digraphic Sequences with Strongly Connected Realizations" . | JOURNAL OF GRAPH THEORY 84 . 2 (2017) : 191-201 . |
| APA | Hong, Yanmei , Liu, Qinghai , Lai, Hong-Jian . Characterization of Digraphic Sequences with Strongly Connected Realizations . | JOURNAL OF GRAPH THEORY , 2017 , 84 (2) , 191-201 . |
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