Search results for "Maximal independent set"
showing 5 items of 5 documents
Neighbor-Distinguishing k-tuple Edge-Colorings of Graphs
2009
AbstractThis paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum numbers of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.
On the chromatic number of disk graphs
1998
Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their different generalizations. For all these graphs including the most general class of the double disk (DD) graphs, it is shown that X(G) ≤ c.ω(G) for a constant c. Several coloring algorithms are analyzed for disk graphs, aiming to improve the bounds on X(G). We find that their worst-case performance expressed in the number of used colors is indeed reached in some instances.
Pattern Matching and Pattern Discovery Algorithms for Protein Topologies
2001
We describe algorithms for pattern-matching and pattern-learning in TOPS diagrams (formal descriptions of protein topologies). These problems can be reduced to checking for subgraph isomorphism and finding maximal common subgraphs in a restricted class of ordered graphs. We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the given set of data. The maximal common subgraph problem then is solved by repeated subgraph extension and checking for isomorphisms. Despite its apparent inefficiency, this approach yields an algorithm with time complexity proportional to the number of graphs in the input set and is still practical on the given set of data. As a…
On the hardness of optimization in power-law graphs
2008
Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks appear to exhibit a power-law distribution: the number of nodes y"i of a given degree i is proportional to i^-^@b where @b>0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization in power-law graphs is easier than in general graphs, prompting the basic theoretical question: Is combinatorial optimization in power-law graphs easy? Does the answer depend on the power-law exponent @b? Our main result is the proof that many classical NP-hard graph-theoretic optimizati…
Bounds for minimum feedback vertex sets in distance graphs and circulant graphs
2008
Graphs and Algorithms