منابع مشابه
Coloring precolored perfect graphs
We consider the question of the computational complexity of coloring perfect graphs with some precolored vertices. It is well known that a perfect graph can be colored optimally in polynomial time. Our results give a sharp border between the polynomial and NP-complete instances, when precolored vertices occur. The key result on the polynomially solvable cases includes a good characterization th...
متن کاملAcyclic edge coloring of 2-degenerate graphs
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). A graph is called 2-degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2-degenerate graphs properly contain...
متن کاملOn Equitable Coloring of d-Degenerate Graphs
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most 1. A d-degenerate graph is a graph G in which every subgraph has a vertex with degree at most d. A star Sm with m rays is an example of a 1-degenerate graph with maximum degree m that needs at least 1 + m/2 colors for an equitable coloring. Our main result is that every n-...
متن کاملGraph coloring , perfect graphs 1 Introduction to graph coloring
Let us improve this bound. Assume that G is a connected graph and T is its spanning tree rooted at r. Let us consider an ordering of V (G) in which each vertex v appears after its children in T . Now, for v 6= r we have |N(vi) ∩ {v1, . . . , vi−1}| ≤ deg v − 1, so c(vi) ≤ deg vi for vi 6= r. Unfortunately, the greedy may still need to use ∆(G) + 1 colors if deg r = ∆(G) and each child of r happ...
متن کاملDefective Coloring on Classes of Perfect Graphs
In Defective Coloring we are given a graph G and two integers χd,∆ ∗ and are asked if we can χd-color G so that the maximum degree induced by any color class is at most ∆∗. We show that this natural generalization of Coloring is much harder on several basic graph classes. In particular, we show that it is NP-hard on split graphs, even when one of the two parameters χd,∆ ∗ is set to the smallest...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00009-x