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Page 1329 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

(D-MUTU; Munich)

*Hamiltonicity**in**graphs**with**few*P,’*s*. (English and German summaries) Computing 54 (1995), no. 3, 213-225. ... 05C45 Ryja¢éek, Zdenék (CZ-WSTB; Pizen)*Hamiltonicity**in*claw-free*graphs*through induced bulls. ...##
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Hamilton cycles in random subgraphs of pseudo-random graphs

2002
*
Discrete Mathematics
*

Given an r-regular

doi:10.1016/s0012-365x(01)00464-2
fatcat:d353rl77mvhdfilq65nusooahe
*graph*G on n vertices*with*a*Hamilton*cycle, order its edges randomly and insert them one by one according to the chosen order, starting from the empty*graph*. ... As a consequence we derive the value of the threshold for the appearance of a*Hamilton*cycle*in*a random subgraph of a pseudo-random*graph*G, satisfying the above stated condition. (A. ... Thus, the corresponding*graph*process problem can be formulated*in*general as follows: given a*graph*G*with*a*Hamilton*cycle, is it true that for almost all*graph*processes (G m ) the ÿrst*Hamilton*cycle ...##
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Optimal covers with Hamilton cycles in random graphs

2014
*
Combinatorica
*

A packing of a

doi:10.1007/s00493-014-2956-z
fatcat:fflvf4odonebdhd6fnwiezxkei
*graph*G*with**Hamilton*cycles is a set of edgedisjoint*Hamilton*cycles*in*G. ... Our proof is based on a result of Knox, Kühn and Osthus on packing*Hamilton*cycles*in*pseudorandom*graphs*. ...*In*that theorem, given a set*S*of vertices*in*a*graph*G, we let N (*S*) denote the external neighbourhood of*S*, i.e. the set of all those vertices x / ∈*S*for which there is some vertex y ∈*S**with*xy ∈ E ...##
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Optimal covers with Hamilton cycles in random graphs
[article]

2013
*
arXiv
*
pre-print

A packing of a

arXiv:1203.3868v2
fatcat:5yqlvgzcdfgttlclt57qe7i6dm
*graph*G*with**Hamilton*cycles is a set of edge-disjoint*Hamilton*cycles*in*G. ... Our proof is based on a result of Knox, Kühn and Osthus on packing*Hamilton*cycles*in*pseudorandom*graphs*. ...*In*that theorem, given a set*S*of vertices*in*a*graph*G, we let N (*S*) denote the external neighbourhood of*S*, i.e. the set of all those vertices x / ∈*S*for which there is some vertex y ∈*S**with*xy ∈ E ...##
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Triangulating graphs with few P4's

1998
*
Discrete Applied Mathematics
*

As a direct application we show how to compute

doi:10.1016/s0166-218x(98)00115-2
fatcat:t34pbiqgsfeohlckipptsxvoim
*in*linear time the minimum fill-*in*and the treewidth of*graphs*whichin a certain local sensecontain only a small number of induced*P4*'*s*. ...*In*this paper we point out the use of the homogeneous decomposition of*graphs*for the purpose of triangulation. ... This comes into line*with*other problems that can be solved*in*linear time on*graphs**with**few*Pd's, e.g. maximum clique, minimum stable set, minimum coloring [3, 201,*hamiltonicity*[ 10, 161, dominating ...##
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On a unique tree representation for P4-extendible graphs

1991
*
Discrete Applied Mathematics
*

Jamison, B. and

doi:10.1016/0166-218x(91)90085-b
fatcat:gk37ridj3bgxnfh7ppmkyjwy3a
*S*. Olariu, On a unique tree representation for*P4*-extendible*graphs*, Discrete Applied Mathematics 34 (1991) 151-164. ... Several practical applications*in*computer science and computational linguistics suggest the study of*graphs*that are unlikely to have more than a*few*induced paths of length three. ... Several practical applications*in*computer science and computational linguistics suggest the study of*graphs*that are unlikely to have more than a*few*induced*P4*'*s*. ...##
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Random graph's Hamiltonicity is strongly tied to its minimum degree
[article]

2019
*
arXiv
*
pre-print

We show that the probability that a random

arXiv:1810.04987v2
fatcat:rr7ieas7trh5dpu2o26jgq5kzu
*graph*G∼ G(n,p) contains no*Hamilton*cycle is (1+o(1))Pr(δ (G) < 2) for all values of p = p(n). We also prove an analogous result for perfect matchings. ... Recall that*in*the proof of Lemma 3.8 we showed that*in*a*graph**with*properties (R1)-(R3), removing a minimum degree vertex yields a*Hamilton*-connected*graph*. ... of*Hamilton*cycles*in*random*graphs*obtained over recent years. ...##
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Author index to volume 191 (1998)

1998
*
Discrete Mathematics
*

Stiebitz, Colour-critical

doi:10.1016/s0012-365x(98)00214-3
fatcat:jf7fdv5bdjf6fn75ffodprouru
*graphs**with**few*edges (1--3} 125 137 Kratochvil, J., Zs. Tuza and M. ... Schelp, Vertex colorings*with*a distance restriction (1-3) 65 82 Fabrici, I. and*S*. ...##
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Page 8601 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

*with*

*few*P,4’

*s*(29-51);

*S*. ... Bylka, Local improving algorithms for large cuts

*in*

*graphs*

*with*maximum degree three (53-67); Kathie Cameron, Thomason’s algorithm for finding a second

*Hamilton*- ian circuit through a given edge

*in*a cubic ...

##
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Finding Hamilton cycles in random intersection graphs
[article]

2017
*
arXiv
*
pre-print

*In*this article we study the problem of finding a

*Hamilton*cycle

*in*a random intersection

*graph*. ... To this end we analyse a classical algorithm for finding

*Hamilton*cycles

*in*random

*graphs*(algorithm HAM) and study its efficiency on

*graphs*from a family of random intersection

*graphs*(denoted here by ... Main results Algorithm HAM, as presented

*in*[6] , is designed to search for a

*Hamilton*cycle

*in*any

*graph*

*with*the minimum degree at least 2. ...

##
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Stability for Vertex Cycle Covers

2017
*
Electronic Journal of Combinatorics
*

$ cycles

doi:10.37236/5185
fatcat:segewcfzsbfdpajj4tnqqotdw4
*in*$G$ that together cover all the vertices.This is tight*in*the sense that there are $n$-vertex*graphs*that have minimum degree $n/k-1$ and that do not contain $k-1$ cycles*with*this property ...*In*1996 Kouider and Lonc proved the following natural generalization of Dirac's Theorem: for any integer $k\geq 2$, if $G$ is an $n$-vertex*graph**with*minimum degree at least $n/k$, then there are $k-1 ... Finally, we will absorb the*few*remaining vertices of G i into the path to get a*Hamilton*path. ...##
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Colour-biased Hamilton cycles in random graphs
[article]

2021
*
arXiv
*
pre-print

We prove that a random

arXiv:2007.12111v4
fatcat:lck23kdkkzemxdcnl6xbnkijrq
*graph*G(n,p),*with*p above the*Hamiltonicity*threshold, is typically such that for any r-colouring of its edges there exists a*Hamilton*cycle*with*at least (2/(r+ 1)-o(1))n edges ... It is natural to expect that if G contains only*few**Hamilton*cycles, then one can r-colour the edges of G*in*such a way that every*Hamilton*cycle sees approximately the same number, i.e. roughly n/r, of ... Write*s*= 1/ε , let t = n/*s*∼ ε n, and let A 1 , . . . , A t , Z be a partitioning of the vertices of G into t "blobs" A i of size*s*and an extra set Z*with*|Z| ≤*s*. ...##
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Random Graph's Hamiltonicity is Strongly Tied to its Minimum Degree

2020
*
Electronic Journal of Combinatorics
*

We show that the probability that a random

doi:10.37236/8339
fatcat:g6rtxyjryvf6rhb3poancmhbce
*graph*$G\sim G(n,p)$ contains no*Hamilton*cycle is $(1+o(1))Pr(\delta (G) < 2)$ for all values of $p = p(n)$. ... Recall that*in*the proof of Lemma 21 we showed that*in*a*graph**with*properties (R1)-(R3), removing a minimum degree vertex yields a*Hamilton*-connected*graph*. ... A*graph*G is*Hamilton*-connected if for every two vertices u, v ∈ V (G), G contains a*Hamilton*path*with*u, v as its two endpoints. Theorem 7. ...##
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Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes
[article]

2018
*
arXiv
*
pre-print

Let {G_i} be the random

arXiv:1710.00799v3
fatcat:ldm7qiptwjhopjpnyghvvzhqma
*graph*process: starting*with*an empty*graph*G_0*with*n vertices,*in*every step i ≥ 1 the*graph*G_i is formed by taking an edge chosen uniformly at random among the non-existing ...*In*particular, we show that the random*graph*process almost surely creates a sequence of*graphs*such that for m ≥ (16 + o(1))n n edges, the 2-core of the*graph*G_m remains Hamiltonian even after an adversary ... The third author would like to thank Michael Krivelevich for directing his attention to [22] which helped*in*making some of the arguments cleaner. ...##
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Master Index: Volumes 81–902-90

1999
*
Discrete Applied Mathematics
*

Olariu, On the structure of

doi:10.1016/s0166-218x(99)80001-8
fatcat:vl4crnxadfhxzflzpbr5qivefq
*graphs**with**few*P& 84 (1998) 1m 13 Babel, L., Triangulating*graphs**with**few**P4*'*s*89 (1998) 45m 57 Balas. E. and M. ... -H., The exact bound of Lee's MLPT Lin, R. and*S*. Olariu, A fast parallel algorithm to recognize*P4*-sparse*graphs*Lippens, P.E.R., see W.F.J. Verhaegh Litman, A., see*S*. Ben-David Litsyn,*S*., P. ...
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