λ-Coloring Matrogenic Graphs
نویسندگان
چکیده
This paper investigates a variant of the general problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph. In our problem, channels assigned to adjacent vertices must be at least two apart, while channels assigned to vertices at distance two must be different. An exact linear time algorithm is provided for the class of threshold graphs. For matrogenic and matroidal graphs approximate algorithms are given. Consequently, previously known results concerning subclasses of cographs, split graphs and graphs with diameter two are improved.
منابع مشابه
-λ coloring of graphs and Conjecture Δ ^ 2
For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...
متن کاملApproximations for λ-Coloring of Graphs
A λ-coloring of a graph G is an assignment of colors from the integer set {0, . . . , λ} to the vertices of the graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-coloring with small or optimal λ arises in the context of radio frequency assignment. We show that the problem of finding the...
متن کاملThe λ-backbone colorings of graphs with tree backbones
The λ-backbone coloring is one of the various problems of vertex colorings in graphs. Given an integer λ ≥ 2, a graph G = (V,E), and a spanning subgraph (backbone) H = (V, EH) of G, a λ-backbone coloring of (G,H) is a proper vertex coloring V → {1, 2, ...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The λ-backbone coloring number BBCλ(G,H) of (G,H) is the s...
متن کاملApproximations for λ-Colorings of Graphs
A λ-coloring of a graph G is an assignment of colors from the integer set {0, . . . , λ} to the vertices of the graph G such that vertices at distance of at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with optimal or near-optimal λ arises in the context of radio frequency assignment. We show that the problem of ...
متن کاملMatroids arisen from matrogenic graphs
Let G be a finite simple graph and let 4(G) be the set of subsets X of V(G) such that the subgraph of G induced by X is threshold. If 4(G) is the independence system of a matroid, then G is called matrogenic [3]. In this paper, we characterize matroids arising from matrogenic graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005