منابع مشابه
On Group Choosability of Total Graphs
In this paper, we study the group and list group colorings of total graphs and present group coloring versions of the total and list total colorings conjectures.We establish the group coloring version of the total coloring conjecture for the following classes of graphs: graphs with small maximum degree, two-degenerate graphs, planner graphs with maximum degree at least 11, planner graphs withou...
متن کاملChoosability, Edge Choosability, and Total Choosability of Outerplane Graphs
Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...
متن کاملTotal Weight Choosability of Graphs
Suppose the edges and the vertices of a simple graph G are assigned k-element lists of real weights. By choosing a representative of each list, we specify a vertex colouring, where for each vertex its colour is defined as the sum of the weights of its incident edges and the weight of the vertex itself. How long lists ensures a choice implying a proper vertex colouring for any graph? Is there an...
متن کاملTotal weight choosability of graphs
A graph G = (V, E) is called (k, k′)-total weight choosable if the following holds: For any total list assignment L which assigns to each vertex x a set L(x) of k real numbers, and assigns to each edge e a set L(e) of k′ real numbers, there is a mapping f : V ∪ E → R such that f(y) ∈ L(y) for any y ∈ V ∪ E and for any two adjacent vertices x, x′, ∑ e∈E(x) f(e)+f(x) 6= ∑ e∈E(x′) f(e)+f(x ′). We ...
متن کاملOn Group Choosability of Graphs, II
Given a group A and a directed graph G, let F(G, A) denote the set of all maps f : E(G) → A. Fix an orientation of G and a list assignment L : V (G) → 2A. For an f ∈ F(G, A), G is (A, L , f )-colorable if there exists a map c : V (G) → ∪v∈V (G)L(v) such that c(v) ∈ L(v), ∀v ∈ V (G) and c(x)− c(y) = f (xy) for every edge e = xy directed from x to y. If for any f ∈ F(G, A), G has an (A, L , f )-c...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2011
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-011-1114-2