Sum List Coloring and Choosability
نویسندگان
چکیده
1
منابع مشابه
k-forested choosability of graphs with bounded maximum average degree
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
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We introduce and study adapted list coloring of graphs and hypergraphs. This is a generalization of ordinary list coloring and adapted coloring, and has more applications than these. We prove that the upper bounds on the adaptable choosability of graphs and uniform hypergraphs in terms of maximum degree are sufficiently stronger than those on the ordinary choosability, while the bounds in terms...
متن کاملSum List Coloring 2*n Arrays
A graph is f -choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number is the minimum over all choosable functions f of the sum of the sizes in f . We show that the sum choice number of a 2 × n array (equivalent to list edge coloring K2,n and to list vertex coloring the cartesian product K22Kn) is n2 ...
متن کاملThe sum choice number of P3 Pn
A graph G is said to be f -choosable if there exists a proper coloring from every assignment of lists of colors to the vertices of G where the list sizes are given by f . The sum choice number of G is the minimum ∑ v∈V (G) f(v) over all f such that G is f -choosable. Here we determine the sum choice of the cartesian product P3 Pn to be 8n − 3 − bn/3c. The techniques used here have applicability...
متن کاملOn the acyclic choosability of graphs
A proper vertex coloring of a graph G = (V, E) is acyclic if G contains no bicolored cycle. A graph G is L-list colorable if for a given list assignment L = {L(v) : v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is L-list colorable for every list assignment with |L(v)| ≥ k for all v ∈ V , then G is said k-choosable. A graph is said to be acyclically k-...
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تاریخ انتشار 2006