The NP-Completeness of Edge-Coloring
نویسنده
چکیده
We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.
منابع مشابه
The NP-completeness of authomorphic colorings
Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic...
متن کاملNP-completeness of list coloring and precoloring extension on the edges of planar graphs
In the edge precoloring extension problem we are given a graph with some of the edges having a preassigned color and it has to be decided whether this coloring can be extended to a proper k-edge-coloring of the graph. In list edge coloring every edge has a list of admissible colors, and the question is whether there is a proper edge coloring where every edge receives a color from its list. We s...
متن کاملComplexity results for minimum sum edge coloring
In the Minimum Sum Edge Coloring problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal. We show that the problem is (a) NP-hard for planar bipartite graphs with maximum degree 3, (b) NP-hard for 3-regular planar graphs, (c) NP-hard for partial 2-trees, and (d) APX-hard for bipartite ...
متن کاملOn the computational complexity of strong edge coloring
In the strong edge coloring problem, the objective is to color the edges of the given graph with the minimum number of colors so that every color class is an induced matching. In this paper, we will prove that this problem is NP-complete even in a very restricted setting. Also, a closely related problem, namely the maximum antimatching problem, is studied, and some NP-completeness results and a...
متن کاملThe complexity of nonrepetitive edge coloring of graphs
A squarefree word is a sequence w of symbols such that there are no strings x, y, and z for which w = xyyz. A nonrepetitive coloring of a graph is an edge coloring in which the sequence of colors along any open path is squarefree. We show that determining whether a graph G has a nonrepetitive k-coloring is Σ p 2 -complete. When we restrict to paths of lengths at most n, the problem becomes NP-c...
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:
- SIAM J. Comput.
دوره 10 شماره
صفحات -
تاریخ انتشار 1981