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- W4385968044 abstract "Given a finite, simple graph $G$, the $k$-component order edge connectivity of $G$ is the minimum number of edges whose removal results in a subgraph for which every component has order at most $k-1$. In general, determining the $k$-component order edge connectivity of a graph is NP-hard. We determine conditions on the vertex degrees of $G$ that can be used to imply a lower bound on the $k$-component order edge connectivity of $G$. We will discuss the process for generating such conditions for a lower bound of 1 or 2, and we explore how the complexity increases when the desired lower bound is 3 or more. In the process, we prove some related results about integer partitions." @default.
- W4385968044 created "2023-08-19" @default.
- W4385968044 creator A5055365665 @default.
- W4385968044 date "2023-08-01" @default.
- W4385968044 modified "2023-10-12" @default.
- W4385968044 title "Component order edge connectivity, vertex degrees, and integer partitions" @default.
- W4385968044 doi "https://doi.org/10.48550/arxiv.2308.00845" @default.
- W4385968044 hasPublicationYear "2023" @default.
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