Browsing by Author "Srikanth, D."

Filter results by typing the first few letters
Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    Ramsey Numbers for Line Graphs
    (2020) Abbasi, H.; Basavaraju, M.; Gurushankar, E.; Jivani, Y.; Srikanth, D.
    Given a graph, the classical Ramsey number R(k,�l) is the least number of vertices that need to be in the graph for the existence of a clique of size k or an independent set of size l. Finding R(k,�l) exactly has been a notoriously hard problem. Even R(k,�3) has not been determined for all values of k. Hence finding the Ramsey number for subclasses of graphs is an interesting question. It is known that even for claw-free graphs, finding Ramsey number is as hard as for general graphs for infinite number of cases. Line graphs are an important subclass of claw-free graphs. The question with respect to line graph L(G) is equivalent to the minimum number of edges the underlying graph G needs to have for the existence of a vertex with degree k or a matching of size l. Chv�tal and Hanson determined this exactly for line graphs of simple graphs. Later Balachandran and Khare gave the same bounds with a different proof. In this paper we find Ramsey numbers for line graph of multi graphs thereby extending the results of Chv�tal and Hanson. Here we determine the maximum number of edges that a multigraph can have, when its matching number, multiplicity, and maximum degree are bounded, and characterize such graphs. � 2020, Springer Nature Switzerland AG.
  • No Thumbnail Available
    Item
    Ramsey Numbers for Line Graphs
    (Springer, 2020) Abbasi, H.; Basavaraju, M.; Gurushankar, E.; Jivani, Y.; Srikanth, D.
    Given a graph, the classical Ramsey number R(k, l) is the least number of vertices that need to be in the graph for the existence of a clique of size k or an independent set of size l. Finding R(k, l) exactly has been a notoriously hard problem. Even R(k, 3) has not been determined for all values of k. Hence finding the Ramsey number for subclasses of graphs is an interesting question. It is known that even for claw-free graphs, finding Ramsey number is as hard as for general graphs for infinite number of cases. Line graphs are an important subclass of claw-free graphs. The question with respect to line graph L(G) is equivalent to the minimum number of edges the underlying graph G needs to have for the existence of a vertex with degree k or a matching of size l. Chvátal and Hanson determined this exactly for line graphs of simple graphs. Later Balachandran and Khare gave the same bounds with a different proof. In this paper we find Ramsey numbers for line graph of multi graphs thereby extending the results of Chvátal and Hanson. Here we determine the maximum number of edges that a multigraph can have, when its matching number, multiplicity, and maximum degree are bounded, and characterize such graphs. © 2020, Springer Nature Switzerland AG.
  • No Thumbnail Available
    Item
    Video Stabilization Using Sliding Frame Window
    (2017) Shagrithaya, K.S.; Gurushankar, E.; Srikanth, D.; Ramteke, P.B.; Koolagudi, S.G.
    Shaky videos are visually unappealing to viewers. Digital video stabilization is a technique to compensate for unwanted camera motion and produce a video that looks relatively stable. In this paper, an approach for video stabilization is proposed which works by estimating a trajectory built by calculating motion between continuous frames using the Shi-Tomasi Corner Detection and Optical Flow algorithms for the entire length of the video. The trajectory is then smoothed using a moving average to give a stabilized output. A smoothing radius is defined, which determines the smoothness of the resulting video. Automatically deciding this parameter�s value is also discussed. The results of stabilization of the proposed approach are observed to be comparable with the state of the art YouTube stabilization. � 2017, Springer International Publishing AG.
  • No Thumbnail Available
    Item
    Video Stabilization Using Sliding Frame Window
    (Springer Verlag service@springer.de, 2017) Shagrithaya, K.S.; Gurushankar, E.; Srikanth, D.; Ramteke, P.B.; Koolagudi, S.G.
    Shaky videos are visually unappealing to viewers. Digital video stabilization is a technique to compensate for unwanted camera motion and produce a video that looks relatively stable. In this paper, an approach for video stabilization is proposed which works by estimating a trajectory built by calculating motion between continuous frames using the Shi-Tomasi Corner Detection and Optical Flow algorithms for the entire length of the video. The trajectory is then smoothed using a moving average to give a stabilized output. A smoothing radius is defined, which determines the smoothness of the resulting video. Automatically deciding this parameter’s value is also discussed. The results of stabilization of the proposed approach are observed to be comparable with the state of the art YouTube stabilization. © 2017, Springer International Publishing AG.