Browsing by Subject "pancyclicity"

Now showing 1 - 5 of 5

Access status: Open Access ,
Edge condition for hamiltonicity in balanced tripartite graphs
(2009) Adamus, Janusz
A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order $2n$ obtained from the complete balanced bipartite $K_{n,n}$ by removing at most $n - 2$ edges, is bipancyclic. We prove an analogous result for balanced tripartite graphs: If $G$ is a balanced tripartite graph of order $3n$ and size at least $3n^{2} - 2n + 2$, then $G$ contains cycles of all lengths.
Access status: Open Access ,
Fan's condition on induced subgraphs for circumference and pancyclicity
(Wydawnictwa AGH, 2017) Wideł, Wojciech
Let $\mathcal{H}$ be a family of simple graphs and $k$ be a positive integer. We say that a graph $G$ of order $n\geq k$ satisfies Fan's condition with respect to $\mathcal{H}$ with constant $k$, if for every induced subgraph $H$ of $G$ isomorphic to any of the graphs from $\mathcal{H}$ the following holds: $\forall u,v\in V(H)\colon d_H(u,v)=2\,\Rightarrow \max\{d_G(u),d_G(v)\}\geq k/2.$ If $G$ satisfies the above condition, we write $G\in\mathcal{F}(\mathcal{H},k)$. In this paper we show that if $G$ is $2$-connected and $G\in\mathcal{F}(\{K_{1,3},P_4\},k)$, then $G$ contains a cycle of length at least $k$, and that if $G\in\mathcal{F}(\{K_{1,3},P_4\},n)$, then $G$ is pancyclic with some exceptions. As corollaries we obtain the previous results by Fan, Benhocine and Wojda, and Ning.
Access status: Restricted ,
Warunek na rozmiar dla długich cykli w grafach dwudzielnych
(Data obrony: 2018-06-22) Głowacz, Diana
Wydział Matematyki Stosowanej
Access status: Restricted ,
Warunki wystarczające na rozmiar dla istnienia cykli w digrafach
(Data obrony: 2012-12-20) Świątkowski, Michał
Wydział Matematyki Stosowanej
Access status: Restricted ,
Zabronione podgrafy gwarantujące pancykliczność
(Data obrony: 2014-10-23) Berek, Katarzyna
Wydział Matematyki Stosowanej