Results 51 to 60 of about 3,567,425 (361)
Discrepancies of spanning trees and Hamilton cycles [PDF]
Journal of Combinatorial Theory, Series B, 2022 We study the multicolour discrepancy of spanning trees and Hamilton cycles in graphs. As our main result, we show that under very mild conditions, the $r$-colour spanning-tree discrepancy of a graph $G$ is equal, up to a constant, to the minimum $s$ such that $G$ can be separated into $r$ equal parts by deleting $s$ vertices.
Lior Gishboliner +2 more
openaire +3 more sources
Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
doaj +1 more source
Hamilton-connected properties in cartesian product [PDF]
Transactions on Combinatorics, 2012 In this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. We present some sufficient and necessary conditions for $GBox H$ being hamilton-connected when $G$ is a hamilton-connected ...
Rushengul Hoshur, Elkin Vumar
doaj
Hamilton cycles in hypergraphs below the Dirac threshold [PDF]
, 2018 We establish a precise characterisation of $4$-uniform hypergraphs with minimum codegree close to $n/2$ which contain a Hamilton $2$-cycle. As an immediate corollary we identify the exact Dirac threshold for Hamilton $2$-cycles in $4$-uniform hypergraphs.
Garbe, Frederik, Mycroft, Richard
core +2 more sources
Large Sets of Hamilton Cycle and Path Decompositions of Complete Bipartite Graphs
Graphs Comb., 2013 In this paper, we determine the existence spectrums for large sets of Hamilton cycle and path (resp. directed Hamilton cycle and path) decompositions of λKm, n (resp. $${\lambda K^{*}_{m,n}}$$).
Hongtao Zhao, Q. Kang
semanticscholar +2 more sources
Perfect Set of Euler Tours of Kp,p,p
Discussiones Mathematicae Graph Theory, 2016 Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence ...
Govindan T., Muthusamy A.
doaj +1 more source
Edge condition for hamiltonicity in balanced tripartite graphs [PDF]
Opuscula Mathematica, 2009 A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order \(2n\) obtained from the complete balanced bipartite \(K_{n,n}\) by removing at most \(n-2\) edges, is bipancyclic.
Janusz Adamus
doaj +1 more source
Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
doaj +1 more source
Packing Loose Hamilton Cycles [PDF]
Combinatorics, Probability and Computing, 2017 A subsetCof edges in ak-uniform hypergraphHis aloose Hamilton cycleifCcovers all the vertices ofHand there exists a cyclic ordering of these vertices such that the edges inCare segments of that order and such that every two consecutive edges share exactly one vertex.
Asaf Ferber +3 more
openaire +3 more sources
Journal of Business Cycle Research, 2020 Within a New Zealand business cycle context, we assess whether Hamilton’s (H84) OLS regression methodology produces stylised business cycle facts which are materially different from the Hodrick–Prescott (HP) and Baxter–King (BK) measures, and whether ...
V. Hall, P. Thomson
semanticscholar +1 more source