![]() ![]() Acan H., Chakraborty S., Jo S., Satti S.R., Succinct encodings for families of interval graphs, Algorithmica 83 ( 2021) 776– 794.Navarro G., Compact Data Structures - A Practical Approach, Cambridge University Press, 2016.Spinrad J.P., Efficient Graph Representations, Fields Institute Monographs, vol.Hajós G., Über eine Art von Graphen, Int.Chakraborty S., Jo S., Compact representation of interval graphs of bounded degree and chromatic number, in: Data Compression Conference, DCC 2022, Snowbird, UT, USA, March 22–25, 2022, IEEE, 2022, pp.Finally, we provide parameterized compact data structures for circular-arc graphs as well with bounded degree or bounded chromatic number condition. Moreover, this takes less space than their data structure when ▪. Unlike the previous upper bound, this data structure is completely new and doesn't follow from the result of Acan et al. Next, we consider the interval graphs with bounded chromatic number ▪, and design a ▪-bit data structure with efficient query times. Note that this upper bound result takes less space than their ( n log 2 n + O ( n ) )-bit upper bound when Δ = O ( n ϵ ), for any 0 < ϵ < 1. ![]() Hence, we provide a compact representation of interval graphs with bounded degree for the first time in literature. (2021), we obtain an ( n log 2 Δ + O ( n ) )-bit data structure supporting the standard navigational queries i.e., degree, adjacency, and neighborhood optimally. Next, by straightforward modifications of the result of Acan et al. First, we show that when the maximum degree of G is bounded by Δ, we show that the space requirement of our data structure is at least ( 1 6 n log 2 Δ − O ( n ) )-bit, which is one of the main contributions of this work. In this paper we initiate the study of designing parameterized compact data structures for an interval graph G with n vertices. ![]()
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