(2,1)-Total labelling of outerplanar graphs
نویسندگان
چکیده
منابع مشابه
Total coloring of pseudo-outerplanar graphs
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-...
متن کاملList total coloring of pseudo-outerplanar graphs
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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It is proved that, if G is a K4-minor-free graph with maximum degree ∆ > 4, then G is totally (∆ + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ∆ + 1 colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours. Together with other known results, t...
متن کاملPathwidth of outerplanar graphs
We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [2], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected...
متن کاملDrawing outerplanar graphs
It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2007
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.07.016