A Result on Line Graphs and Hamiltonian Graphs
نویسندگان
چکیده
منابع مشابه
On s-Hamiltonian Line Graphs
For an integer s ≥ 0, a graph G is s-hamiltonian if for any vertex subset S′ ⊆ V (G) with |S′| ≤ s, G − S′ is hamiltonian. It is well known that if a graph G is s-hamiltonian, then G must be (s + 2)-connected. The converse is not true, as there exist arbitrarily highly connected nonhamiltonian graphs. But for line graphs, we prove that when s ≥ 5, a line graph is s-hamiltonian if and only if it...
متن کاملHamiltonian Connected Line Graphs
Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5−E(C), where C is a cycle of length 4 in K5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass-free line graph is ...
متن کاملA result on Hamiltonian line graphs involving restrictions on induced subgraphs
It is shown that the existence of a Hamilton cycle in the line graph of a graph G can be ensured by imposing certain restrictions on certain induced subgraphs of G. Thereby a number of known results on hamiltonian line graphs are improved, including the earliest results in terms of vertex degrees. One particular consequence is that every graph of diameter 2 and order at least 4 has a hamiltonia...
متن کاملOn 3-connected hamiltonian line graphs
Thomassen conjectured that every 4-connected line graph is hamiltonian. It has been proved that every 4-connected line graph of a claw-free graph, or an almost claw-free graph, or a quasi-claw-free graph, is hamiltonian. In 1998, Ainouche et al. [2] introduced the class of DCT graphs, which properly contains both the almost claw-free graphs and the quasi-claw-free graphs. Recently, Broersma and...
متن کاملOn s-hamiltonian-connected line graphs
1 A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton 2 path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion 3 of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this 4 paper, we prove that the line graph of a (t+4)-edge-connected graph is (t+2)-hamiltonian5 connected if and only ...
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ژورنال
عنوان ژورنال: International Journal of Computer Applications
سال: 2015
ISSN: 0975-8887
DOI: 10.5120/21055-3703