Distances in cocomparability graphs and their powers
Discrete Applied Mathematics
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Scheduling algorithms for multihop radio networks
IEEE/ACM Transactions on Networking (TON)
Powers of distance-hereditary graphs
Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On powers of circular arc graphs and proper circular arc graphs
Discrete Applied Mathematics
Homogeneously orderable graphs
Theoretical Computer Science
The algorithmic use of hypertree structure and maximum neighbourhood orderings
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Graph classes: a survey
Weakly chordal graph algorithms via handles
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
NP-Completeness Results and Efficient Approximations for Radiocoloring in Planar Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
LexBFS-Ordering in Asteroidal Triple-Free Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Fixed-Parameter Complexity of lambda-Labelings
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Channel Assignment with Separation for Interference Avoidance in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics
Coloring Powers of Chordal Graphs
SIAM Journal on Discrete Mathematics
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
New min-max theorems for weakly chordal and dually hordal graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Hi-index | 0.00 |
Motivated by the frequency assignment problem in heterogeneous multihop radio networks, where different radio stations may have different transmission ranges, we introduce two new types of coloring of graphs, which generalize the well-known Distance-k-Coloring. Let G=(V,E) be a graph modeling a radio network, and assume that each vertex v of G has its own transmission radius r(v), a non-negative integer. We define r-coloring (r+-coloring) of G as an assignment Φ: V↦{0,1,2,...} of colors to vertices such that Φ(u)=Φ(v) implies dG(u,v)r(v)+r(u) (dG(u,v)r(v)+r(u)+1, respectively). The r-Coloring problem (the r+-Coloring problem) asks for a given graph G and a radius-function r: V↦N∪{0}, to find an r-coloring (an r+-coloring, respectively) of G with minimum number of colors. Using a new notion of generalized powers of graphs, we investigate the complexity of the r-Coloring and r+-Coloring problems on several families of graphs