A combinatorial bijection between linear extensions of equivalent orders
Discrete Mathematics
Algorithmic graph theory
The Hamiltonian circuit problem for circle graphs in NP-complete
Information Processing Letters
Linear algorithm for optimal path cover problem on interval graphs
Information Processing Letters
Optimal covering of cacti by vertex-disjoint paths
Theoretical Computer Science
An O(n2 log n) algorithm for the Hamiltonian cycle problem on circular-arc graphs
SIAM Journal on Computing
Polynomial Algorithms for Hamiltonian Cycle in Cocomparability Graphs
SIAM Journal on Computing
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Optimal Solution for the Channel-Assignment Problem
IEEE Transactions on Computers
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In this paper, the order-theoretic problem of finding linear extensions of a partially ordered set (POSet) with certain properties is mapped to the corresponding graphtheorectic problem. Given a POSet, a jump exists between two consecutive symbols in a topological sequence if there is no relation between these two symbols in the POSet. We want to find a topological sequence that minimizes or maximizes the total number of jumps. In graph-theoretic terms, define the jump number optimization problem as finding a linear ordering of vertex sequence of a graph such that the number of pairs of consecutive vertices that are adjacent is maximized (jump number minimization problem) or minimized (jump number maximization problem). The complexities of both problems with respect to some special graphs are investigated first in this paper. We then study the jump maximization problem for proper interval graphs and series-parallel graphs. From this study, we hope that more researches can be derived from these interdisciplinary knowledge domains.