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Equitable partition of plane graphs with independent crossings into induced forests

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arxiv 1903.08337 v2 pith:4UE7WT3R submitted 2019-03-20 math.CO cs.DM

Bei Niu , Xin Zhang , Yuping Gao This is my paper · ORCID
classification math.COcs.DM
keywords crossingsgraphindependentplaneequitableforestsinducedpartition
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abstract

The cluster of a crossing in a graph drawing in the plane is the set of the four end-vertices of its two crossed edges. Two crossings are independent if their clusters do not intersect. In this paper, we prove that every plane graph with independent crossings has an equitable partition into $m$ induced forests for any $m\geq 8$. Moreover, we decrease this lower bound 8 for $m$ to 6, 5, 4 and 3 if we additionally assume that the girth of the considering graph is at least 4, 5, 6 and 26, respectively.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Equitable tree-$O(d)$-coloring of $d$-degenerate graphs

    math.CO 2019-08 conditional novelty 7.0 of 10

    Every d-degenerate graph with at least beta-Delta vertices has an equitable tree-k-coloring for every k at least alpha-d, for twelve explicit (alpha, beta) pairs such as (8,56) and (52,6).

  2. Equitable partition of graphs into induced linear forests

    math.CO 2019-08 accept novelty 6.0 of 10

    The vertex set of any simple graph admits an equitable partition into k induced linear forests for every k at least max of ceil((Δ(G)+1)/2) and ceil(|G|/4).

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