Feasible edge colorings of trees with cardinality constraints
نویسندگان
چکیده
A variation of preemptive open shop scheduling corresponds to nding a feasible edge coloring in a bipartite multigraph with some requirements on the size of the di erent color classes. We show that for trees with xed maximum degree, one can nd in polynomial time an edge k-coloring where for i = 1; : : : ; k the number of edges of color i is exactly a given number hi, and each edge e gets its color from a set ’(e) of feasible colors, if such a coloring exists. This problem is NP-complete for general bipartite multigraphs. Applications to open shop problems with costs for using colors are described. c © 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
Mixed Roman domination and 2-independence in trees
Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. A {em mixed Roman dominating function} (MRDF) of $G$ is a function $f:Vcup Erightarrow {0,1,2}$ satisfying the condition that every element $xin Vcup E$ for which $f(x)=0$ is adjacentor incident to at least one element $yin Vcup E$ for which $f(y)=2$. The weight of anMRDF $f$ is $sum _{xin Vcup E} f(x)$. The mi...
متن کاملA Partitioning Scheme for Solving the 0-1 Knapsack Problem
The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth [13] included cardin...
متن کاملConflict-Free Colorings - Of Graphs and Hypergraphs - Diploma-Thesis of
Conflict-free colorings are known as vertex-colorings of hypergraphs. In such a coloring each hyperedge contains a vertex whose color is not assigned to any other vertex within this edge. In this thesis the notion of conflict-free colorings is translated to edge-colorings of graphs. For graphs G and H a conflict-free coloring of G ensures an edge of unique color in each copy of H in G. The mini...
متن کاملEternal m-security subdivision numbers in graphs
An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...
متن کاملEdge colorings of complete graphs without tricolored triangles
We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size of largest monochromatic stars guaranteed to occur. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 211–216, 2004
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:
- Discrete Mathematics
دوره 222 شماره
صفحات -
تاریخ انتشار 2000