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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)
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)
The well-known Chvátal–Erd˝ os 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)
The square of a graph is obtained by adding additional edges joining all pair of vertices of distance two in the original graph. Particularly, if C is a hamiltonian cycle of a graph G, then the square of C is called a hamiltonian square of G. In this paper, we characterize all possible forbidden pairs, which implies the containment of a hamiltonian square,(More)
Let G be a simple graph of order n, and let ∆(G) and χ ′ (G) denote the maximum degree and chromatic index of G, respectively. Vizing proved that χ ′ (G) = ∆(G) or ∆(G) + 1. Following this result, G is called edge-chromatic critical if χ ′ (G) = ∆(G) + 1 and χ ′ (G − e) = ∆(G) for every e ∈ E(G). In 1968, Vizing conjectured that if G is edge-chromatic(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)
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)
Corrádi and Hajnal [1] showed that any graph of order at least 3k with minimum degree at least 2k contains k vertex-disjoint cycles. This minimum degree condition is sharp, because the complete bipartite graph K 2k−1,n−2k+1 does not contain k vertex-disjoint cycles. About the existence of vertex-disjoint cycles of the same length, Thomassen [4] conjectured(More)