Showing papers by "Deepak Rajendraprasad published in 2020"
Posted Content•
TL;DR: In this paper, the authors improved the upper bound to $ 1.373 d^2 + 6.971d-1, which is the best known upper bound for the family of graphs with diameter greater than or equal to 8.
Abstract: An orientation of an undirected graph $G$ is an assignment of exactly one direction to each edge of $G$. The oriented diameter of a graph $G$ is the smallest diameter among all the orientations of $G$. The maximum oriented diameter of a family of graphs $\mathscr{F}$ is the maximum oriented diameter among all the graphs in $\mathscr{F}$. Chvatal and Thomassen [JCTB, 1978] gave a lower bound of $\frac{1}{2}d^2+d$ and an upper bound of $2d^2+2d$ for the maximum oriented diameter of the family of $2$-edge connected graphs of diameter $d$. We improve this upper bound to $ 1.373 d^2 + 6.971d-1 $, which outperforms the former upper bound for all values of $d$ greater than or equal to $8$. For the family of $2$-edge connected graphs of diameter $3$, Kwok, Liu and West [JCTB, 2010] obtained improved lower and upper bounds of $9$ and $11$ respectively. For the family of $2$-edge connected graphs of diameter $4$, the bounds provided by Chvatal and Thomassen are $12$ and $40$ and no better bounds were known. By extending the method we used for diameter $d$ graphs, along with an asymmetric extension of a technique used by Chvatal and Thomassen, we have improved this upper bound to $21$.
8 citations
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TL;DR: This work characterizes B$_0$-VPG cocomparability graphs and develops a drawing algorithm for the class that can distinguish comparable pairs from incomparable ones and identify which among a comparable pair is larger in $P$ from this visualization.
Abstract: B$_0$-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B$_0$-VPG permutation graphs. We respond here by characterizing B$_0$-VPG cocomparability graphs. This characterization also leads to a polynomial time recognition and B$_0$-VPG drawing algorithm for the class. Our B$_0$-VPG drawing algorithm starts by fixing any one of the many posets $P$ whose cocomparability graph is the input graph $G$. The drawing we obtain not only visualizes $G$ in that one can distinguish comparable pairs from incomparable ones, but one can also identify which among a comparable pair is larger in $P$ from this visualization.
3 citations
16 Sep 2020
TL;DR: In this article, a polynomial time algorithm for the class of VPG cocomparability graphs is proposed. But the algorithm requires the graph to be a permutation of the input graph.
Abstract: \(B_{0}\)-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B\(_{0}\)-VPG permutation graphs. We respond here by characterizing B\(_{0}\)-VPG cocomparability graphs. This characterization also leads to a polynomial time recognition and B\(_{0}\)-VPG drawing algorithm for the class. Our B\(_{0}\)-VPG drawing algorithm starts by fixing any one of the many posets P whose cocomparability graph is the input graph G. The drawing we obtain not only visualizes G in that one can distinguish comparable pairs from incomparable ones, but one can also identify which among a comparable pair is larger in P from this visualization.
2 citations
13 Feb 2020
TL;DR: A new distributed routing algorithm is proposed for the same unidirectional star graph, called S_n, analysed by Fujita, which routes a packet from any node £s to any node $t at an undirected distance from $s using at most $\min\{4d+4, 2n+4\}$ hops.
Abstract: An orientation of an undirected graph G is an assignment of exactly one direction to each edge of G. Converting two-way traffic networks to one-way traffic networks and bidirectional communication networks to unidirectional communication networks are practical instances of graph orientations. In these contexts minimising the diameter of the resulting oriented graph is of prime interest.
1 citations
Posted Content•
TL;DR: It is shown that for each non-negative integer k, every bipartite tournament either contains k arc-disjoint cycles or has a feedback arc set of size at most 7(k - 1).
Abstract: We show that for each non-negative integer k, every bipartite tournament either contains k arc-disjoint cycles or has a feedback arc set of size at most 7(k - 1).