Choosability of a weighted path and free-choosability of a cycle
نویسندگان
چکیده
A graph G with a list of colors L(v) and weight w(v) for each vertex v is (L,w)-colorable if one can choose a subset of w(v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be (L,w)-colorable for some list assignments L. Furthermore, we solve the problem of the free-choosability of a cycle.
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...
متن کاملExtended core and choosability of a graph
A graph G is (a, b)-choosable if for any color list of size a associated with each vertices, one can choose a subset of b colors such that adjacent vertices are colored with disjoint color sets. This paper shows an equivalence between the (a, b)-choosability of a graph and the (a, b)-choosability of one of its subgraphs called the extended core. As an application, this result allows to prove th...
متن کاملFree Choosability of Outerplanar Graphs
AgraphG is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex u = v, the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free (a, b)-choosable is given. As a corollar...
متن کاملTriangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count
We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter D = Ω( √ n), and at most min ( 2n−Ω( √ n), 2n−D − 2 ) edges.
متن کاملChoosability on H-free graphs
A graph is H-free if it has no induced subgraph isomorphic to H. We determine the computational complexity of the Choosability problem restricted to H-free graphs for every graph H that does not belong to {K1,3, P1 +P2, P1 +P3, P4}. We also show that if H is a linear forest, then the problem is fixed-parameter tractable when parameterized by k.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1005.5602 شماره
صفحات -
تاریخ انتشار 2010