Edge covering pseudo-outerplanar graphs with forests
نویسندگان
چکیده
منابع مشابه
Edge covering pseudo-outerplanar graphs with forests
A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, we prove that each pseudo-outerplanar graph admits edge decompositions into a linear forest and an outerplanar graph, or a star forest and an outerpla...
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A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, the total coloring conjecture is completely confirmed for pseudoouterplanar graphs. In particular, it is proved that the total chromatic number of every pseudo-...
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A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. It is proved that every pseudo-outerplanar graph with maximum degree ∆ ≥ 5 is totally (∆ + 1)-choosable.
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We prove that every planar graphs has an edge partition into three forests, one having maximum degree 4. This answers a conjecture of Balogh et al. (J. Combin. Theory B. 94 (2005) 147-158).We also prove that every planar graphs with girth g ≥ 6 (resp. g ≥ 7) has an edge partition into two forests, one having maximum degree 4 (resp. 2).
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.05.017