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- W217893412 abstract "Let $G$ be an $n$-vertex graph with $nge 3$. A classic result of Dirac from 1952 asserts that $G$ is hamiltonian if $delta(G)ge n/2$. Dirac's theorem is one of the most influential results in the study of hamiltonicity and by now there are many related known results,(see, e.g., J. A. Bondy, Basic Graph Theory: Paths and Circuits, Chapter 1 in: {it Handbook of Combinatorics Vol.1}). A {it Halin graph} is a planar graph consisting of two edge-disjoint subgraphs: a spanning tree of at least 4 vertices and with no vertex of degree 2, and a cycle induced on the set of the leaves of the spanning tree. Halin graphs possess rich hamiltonicity properties such as being hamiltonian, hamiltonian connected, and almost pancyclic. As a continuous generalization of Dirac's theorem, in this paper, we show that there exists a positive integer $n_0$ such that any graph $G$ with $nge n_0$ vertices and $delta(G)ge (n+1)/2$ contains a spanning Halin subgraph. In particular, it contains a spanning Halin subgraph which is also pancyclic." @default.
- W217893412 created "2016-06-24" @default.
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- W217893412 date "2015-05-22" @default.
- W217893412 modified "2023-10-14" @default.
- W217893412 title "Dirac's Condition for Spanning Halin Subgraphs" @default.
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- W217893412 doi "https://doi.org/10.48550/arxiv.1505.06181" @default.
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