9,485 research outputs found
Signless Laplacian spectral radius for a k-extendable graph
Let and be two nonnegative integers with (mod 2), and let
be a graph of order with a 1-factor. Then is said to be
-extendable for if every matching in of size
can be extended to a 1-factor. In this paper, we first establish a lower
bound on the signless Laplacian spectral radius of to ensure that is
-extendable. Then we create some extremal graphs to claim that all the
bounds derived in this article are sharp.Comment: 11 page
Hamiltonian chordal graphs are not cycle extendible
In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle
extendible; that is, the vertices of any non-Hamiltonian cycle are contained in
a cycle of length one greater. We disprove this conjecture by constructing
counterexamples on vertices for any . Furthermore, we show that
there exist counterexamples where the ratio of the length of a non-extendible
cycle to the total number of vertices can be made arbitrarily small. We then
consider cycle extendibility in Hamiltonian chordal graphs where certain
induced subgraphs are forbidden, notably and the bull.Comment: Some results from Section 3 were incorrect and have been removed. To
appear in SIAM Journal on Discrete Mathematic
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