Article in volume
Authors:
Title:
Chorded $k$-pancyclic and weakly $k$-pancyclic graphs
PDFSource:
Discussiones Mathematicae Graph Theory 44(1) (2024) 337-350
Received: 2021-09-27 , Revised: 2022-01-09 , Accepted: 2022-01-10 , Available online: 2022-02-08 , https://doi.org/10.7151/dmgt.2449
Abstract:
As natural relaxations of pancyclic graphs, we say a graph $G$ is $k$-pancyclic
if $G$ contains cycles of each length from $k$ to $|V(G)|$ and $G$ is
weakly pancyclic if it contains cycles of all lengths from the girth to
the circumference of $G$, while $G$ is weakly $k$-pancyclic if it contains
cycles of all lengths from $k$ to the circumference of $G$. A cycle $C$ is
chorded if there is an edge between two vertices of the cycle that is not an
edge of the cycle. Combining these ideas, a graph is chorded pancyclic if
it contains chorded cycles of each length from $4$ to the circumference of the
graph, while $G$ is chorded $k$-pancyclic if there is a chorded cycle of
each length from $k$ to $|V(G)|$. Further, $G$ is chorded weakly
$k$-pancyclic if there is a chorded cycle of each length from $k$ to the
circumference of the graph. We consider conditions for graphs to be chorded
weakly $k$-pancyclic and chorded $k$-pancyclic.
Keywords:
cycle, chord, pancyclic, weakly pancyclic
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