Partitioning a graph into a cycle and a sparse graph
نویسندگان
چکیده
In this paper we investigate results of the form “every graph G has a cycle C such that induced subgraph on V(G)∖V(C) small maximum degree.” Such haven't been studied before, but are motivated by Bessy and Thomassé Theorem which states vertices any can be covered C1 in disjoint C2 complement G. There two main theorems paper. The first is every with Δ(G[V(G)∖V(C)])≤12(|V(G)∖V(C)|−1). bound degree Δ(G[V(G)∖V(C)]) best possible. second theorem k-connected Δ(G[V(G)∖V(C)])≤1k+1|V(G)∖V(C)|+3. We also give an application to conjecture about partitioning edge-coloured complete graphs into monochromatic cycles.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2023
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2022.113161