论文标题
确切的计数$ c_ {4} $ s在爆炸图中
Exact Counts of $C_{4}$s in Blow-Up Graphs
论文作者
论文摘要
周期具有许多有趣的特性，并在许多学科中进行了广泛的研究。在某些领域，最大化$ k $ - 周期的计数特别令人感兴趣。 \ emph {blow-up}方法是用于最大化子图$ h $的构建方法的自然候选者。在$ n $顶点上以图形$ g $和图案图$ h $上的图形图$ h $上的$ k $顶点，以便$ n \ geq k $，爆炸方法涉及一个迭代过程，以$ g $ $ g $替换$ g $的过程，并使用$ k $ vertex Graph $ h $更换$ g $。在本文中，我们将爆炸方法应用于周期家族。然后，我们介绍长度4的确切计数，用于在周期和广义theta图上使用这种爆炸方法。
Cycles have many interesting properties and are widely studied in many disciplines. In some areas, maximising the counts of $k$-cycles are of particular interest. A natural candidate for the construction method used to maximise the number of subgraphs $H$ in a graph $G$, is the \emph{blow-up} method. Take a graph $G$ on $n$ vertices and a pattern graph $H$ on $k$ vertices, such that $n\geq k$, the blow-up method involves an iterative process of replacing vertices in $G$ with a copy of the $k$-vertex graph $H$. In this paper, we apply the blow-up method on the family of cycles. We then present the exact counts of cycles of length 4 for using this blow-up method on cycles and generalised theta graphs.
