deciding graph non-hamiltonicity via a closure algorithm
Authors
abstract
we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set e, whose members are pairs of components of p, {pu,i, pv,i+1}, i = 1, n - 1, for each arc (u, v) not in
similar resources
Deciding Graph non-Hamiltonicity via a Closure Algorithm
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set ...
full textDeciding Graph non-Hamiltonicity via a Closure Algorithm
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n+ 1 vertices corresponds with each of the n! n-permutation matrices P , such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+ 1. A graph instance (G) is initially coded as exclusion set E...
full textA Non-Hamiltonicity Proof System
To date, the field of proof complexity contains only one major example of a graph theoretic proof system, the Hajós Calculus. With the goal of further diversifying the field of proof complexity, we describe the ‘Non-Hamiltonicity Proof System’ (NHPS), for which we prove soundness, completeness, exponential lower bounds on necessary proof length, as well as a simulation by Tree Resolution.
full textA Simple Algorithm for Hamiltonicity
We develop a new algebraic technique that solves the following problem: Given a black box that contains an arithmetic circuit f over a field of characteristic 2 of degree d. Decide whether f , expressed as an equivalent multivariate polynomial, contains a multilinear monomial of degree d. This problem was solved by Williams [4] and Björklund et. al. [5] for a white box (the circuit is given as ...
full textClosure and Forbidden Pairs for Hamiltonicity
Let C be the claw K 1;3 and N the net, i.e. the only connected graph with degree sequence 333111. It is known Bedrossian 1991; Faudree and Gould 1997] that if X; Y is a pair of connected graphs such that, for any 2-connected graph G, G being X Y-free implies G is hamiltonian, then X is the claw C and Y belongs to a nite list of graphs, one of them being the net N. For any such pair X; Y we show...
full textA Simple Algorithm for Undirected Hamiltonicity
We develop a new algebraic technique that gives a simple randomized algorithm for the simple k-path problem with the same complexity O∗(1.657k) as in [1] and [3].
full textMy Resources
Save resource for easier access later
Journal title:
journal of algorithms and computationجلد ۴۸، شماره ۱، صفحات ۱-۳۵
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023