Let f(n) be the smallest integer such that for every graph G of order n with minimum degree δ(G) > f(n), the line graph L(G) of G is pancyclic whenever L(G) ...
A graph of order n is pancyclic if it contains Ck, i.e., a cycle of length k, for each k with 3 ~< k ~< n. A natural question is the following: how large should ...
Sep 7, 2022 · An n-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is pancyclic if it contains cycles of all lengths from 3 up to ...
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A related notion to Hamiltonicity is that of pancyclicity. An n-vertex graph is said to be pancyclic if it contains all cycles of length from 3 up to n.
A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length ` for all 3 ≤ ` ≤ n.
In this thesis, we work on generalizations of hamiltonian graph theory, and focus on the following topics: hamiltonian, pancyclicity, chorded pancyclic in the ...
Jul 20, 2023 · An n-vertex graph is said to be pancyclic if it contains all cycles of length from 3 up to n. Trivially, pancyclicity is a stronger property ...
Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) ...
We prove lower bounds on the number of different cycle lengths of cubic Hamiltonian graphs that do not contain a fixed subdivision of a claw as an induced ...
This paper shows that if G is a connected graph of order n such that and L(G) is hamiltonian, then, for n ≥ 43, L(G) is pancyclic.