Songling Shan

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We show that if G is a graph such that every edge is in at least two triangles, then G contains a spanning tree with no vertex of degree 2 (a homeomorphically irreducible spanning tree). This result was originally asked in a question format by Albertson, Berman, Hutchinson, and Thomassen in 1979, and then conjectured to be true by Archdeacon in 2009.(More)
A spanning tree T of a graph G is called a homeomorphically irreducible spanning tree (HIST) if T does not contain vertices of degree 2. A graph G is called locally connected if for every vertex v ∈ V (G), the subgraph induced by the neighborhood of v is connected. In this paper, we prove that every connected and locally connected graph with more than 3(More)
The well-known Chvátal–Erdős Theorem states that every graph G of order at least three with α(G) ≤ κ(G) has a hamiltonian cycle, where α(G) and κ(G) are the independence number and the connectivity of G, respectively. Oberly and Sumner [J. Graph Theory 3 (1979), 351–356] have proved that every connected, locally-connected claw-free graph of order at least(More)
In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersection. This is not true in general and various counterexamples have been found. However, the answer to Gallai’s question is positive for several well-known classes of graphs, as for instance connected outerplanar graphs, connected split graphs, and 2-trees. A graph is(More)
Anomaly detection is an important component of computer security defense. As the security situation becomes increasingly severe, abnormality is detected by the sequential pattern mining has become a hot research topic. For normal behavior to identify in anomaly detection, proposed software behavior pattern recognition technology which based on improved(More)
In recent years, the web security events emerge in endlessly, web security has been widely concerned. Among these web security flaws, defects of unchecked input occupy the majority. The unchecked input defect refers to not reasonable verification of input from users and the environment, which will cause the system to be used by attackers. This paper mainly(More)
Aiming at the PrefixSpan algorithm produce huge amount of project databases in mining sequence patterns, this paper proposes an Improved PrefixSpan algorithm for Mining Sequential Patterns(IPMSP) algorithm. By avoid produce duplicated project databases with the same prefix pattern through checking the prefix with regard to prefix of the sequence database(More)