A note on entire choosability of plane graphs
نویسندگان
چکیده
منابع مشابه
A note on face coloring entire weightings of plane graphs
Given a weighting of all elements of a 2-connected plane graph G = (V,E, F ), let f(α) denote the sum of the weights of the edges and vertices incident with the face α and also the weight of α. Such an entire weighting is a proper face colouring provided that f(α) 6= f(β) for every two faces α and β sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring...
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It is proved that if G is a plane embedding of a K4-minor-free graph with maximum degree ∆, then G is entirely 7-choosable if ∆ ≤ 4 and G is entirely (∆+2)-choosable if ∆ ≥ 5; that is, if every vertex, edge and face of G is given a list of max{7,∆+2} colours, then every element can be given a colour from its list such that no two adjacent or incident elements are given the same colour. It is pr...
متن کاملThe edge-face choosability of plane graphs
A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)| = k for every edge and face x , there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree ∆(G) is (∆(G)+ 3)-edge-face choosable. © 2004 Elsevier ...
متن کاملEntire Labeling of Plane Graphs
A face irregular entire k-labeling φ : V ∪E ∪F → {1,2, . . . ,k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wφ ( f ) and wφ (g) are distinct. The weight of a face f under a k-labeling φ is the sum of labels carried by that face and all the edges and vertices incident with the face....
متن کاملOn Structure of Some Plane Graphs with Application to Choosability
A graph G=(V, E) is (x, y)-choosable for integers x> y 1 if for any given family [A(v) | v # V] of sets A(v) of cardinality x, there exists a collection [B(v) | v # V] of subsets B(v)/A(v) of cardinality y such that B(u) & B(v)=< whenever uv # E(G). In this paper, structures of some plane graphs, including plane graphs with minimum degree 4, are studied. Using these results, we may show that if...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.12.014