Efficient algorithm for the vertex connectivity of trapezoid graphs
نویسندگان
چکیده
منابع مشابه
Efficient algorithm for the vertex connectivity of trapezoid graphs
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing problems in VLSI design and identifying the optimal chain of non-overlapping fragments in bioinformatics. Using modified binary indexed tree data structure, we de...
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Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the complement has a transitive orientation). The operation of “vertex splitting”, introduced in [3], f...
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Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
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The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of minimum vertex covers (or independent sets), as well as the total number of vertex covers, and reduce the time complexity from O(n) to O(n log n), where n is the...
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C1. The input graph cannot be modified; its integrity must be preserved. C2. The processing unit has a “small” memory space (compared to the huge size of the graph). C3. The solution must be sent piece by piece to an external memory as soon as it is produced. Constraint C2 implies that the graph cannot be loaded into the memory of the processing unit. The constraint C3 comes from the fact that ...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2013
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2013.02.012