A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A note on path-perfect graphs

1981
*
Discrete Mathematics
*

It is

doi:10.1016/0012-365x(81)90262-4
fatcat:tqguvyeltve4nlblukdraa2hha
*noted*that the<*graphs*I&, K(r, 2r -1) and K(r, 2r+ ?I are*path*-*perfect*. Also some resuk are given concerning the existen* of regular*path*-*perfect**graphs*. ... In this paper we explore the c:oncept of factoring*a**graph*into non-isomorphic*paths*. Lel Pi denote the*path*of length i. ...*A*lstence of re; ;ular pathperfect*graphs*-wk en 1' is odd and r divides neither n l;lor n + 1. Rx example, doses there exist*a*15regular*path*-*perfect**graph*of 019er 25 and size 210'? ...##
###
Average connectivity and average edge-connectivity in graphs

2013
*
Discrete Mathematics
*

In addition, we show that this family has the fewest

doi:10.1016/j.disc.2013.05.024
fatcat:watglpdtynbprf3fdrnjqdvvgy
*perfect*matchings among cubic*graphs*that have*perfect*matchings. ... Connectivity and edge-connectivity of*a**graph*measure the difficulty of breaking the*graph*apart, but they are very much affected by local aspects like vertex degree. ... Recall that every vertex in R has exactly*one*neighbor in S. For the vertex after u*on**a*u, v-*path*, at most*one*vertex of S is available. ...##
###
Partial and perfect path covers of cographs

1998
*
Discrete Applied Mathematics
*

*A*set r/P of disjoint

*paths*in

*a*

*graph*G is called

*a*(complete)

*path*cover of G if every vertex of G belongs to

*one*of the

*paths*in :fl. ... In this paper, we introduce

*a*variant of

*a*minimum

*path*cover, called

*a*

*perfect*

*path*cover. ... Recall that our construction of

*a*

*perfect*

*path*cover of

*a*product

*graph*depends only

*on*the

*perfect*

*path*cover of its largest factor. ...

##
###
On perfect colorings of infinite multipath graphs

2020
*
Sibirskie Elektronnye Matematicheskie Izvestiya
*

We consider

doi:10.33048/semi.2020.17.139
fatcat:zou3m5yqrfguldtd7i2lsfe5ia
*a*lexicographic product of the innite*path**graph*and*a**graph*G that can be either the complete or empty*graph**on*n vertices. ...*A*coloring of vertices of*a*given*graph*is called*perfect*if the color structure of each sphere of radius 1 in the*graph*depends only*on*the color of the sphere center. Let n be*a*positive integer. ... There is*a**one*-to-*one*correspondence between the*perfect*colorings of an innite*path**graph*and the block-monochrome*perfect*colorings of C ∞ · K n and C ∞ · K n ; the latter are obtained by K n -times ...##
###
Extending Maximal Perfect Haplotype Blocks to the Realm of Pangenomics
[chapter]

2020
*
Lecture Notes in Computer Science
*

We define

doi:10.1007/978-3-030-42266-0_4
fatcat:on7iacahxnhivpauodh66cqdy4
*a*maximal*perfect*pangenome haplotype block and give*a*lineartime, suffix tree based approach to find all such blocks from*a*set of pangenome haplotypes. ... We demonstrate the method by applying it to*a*pangenome built from yeast strains. ...*A*bubble in*a*De Bruijn*graph*that represents*a*SNP; we arbitrarily consider*one*side of the bubble to be the '0'*path*and the other to be the '1'*path*. ...##
###
Finding Induced Paths of Given Parity in Claw-Free Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

Finally, we show that

doi:10.1007/978-3-642-11409-0_30
fatcat:hstidpzhcjgvzka2vl6sd6yxma
*a*shortest induced*path*of given parity between two specified vertices of*a*claw-free*perfect**graph*can be found in O(n 7 ) time. An extended abstract of this paper has been ... The Parity*Path*problem is to decide if*a*given*graph*contains both an induced*path*of odd length and an induced*path*of even length between two specified vertices. ... They present an O(|G|m + n) time algorithm for the Group*Path*problem*on*chordal*graphs*using*a**perfect*elimination ordering. ...##
###
Finding Induced Paths of Given Parity in Claw-Free Graphs

2010
*
Algorithmica
*

Finally, we show that

doi:10.1007/s00453-010-9470-5
fatcat:emwqsmiedbfrnc4qd35kei5xki
*a*shortest induced*path*of given parity between two specified vertices of*a*claw-free*perfect**graph*can be found in O(n 7 ) time. An extended abstract of this paper has been ... The Parity*Path*problem is to decide if*a*given*graph*contains both an induced*path*of odd length and an induced*path*of even length between two specified vertices. ... They present an O(|G|m + n) time algorithm for the Group*Path*problem*on*chordal*graphs*using*a**perfect*elimination ordering. ...##
###
A note on internally disjoint alternating paths in bipartite graphs

2005
*
Discrete Mathematics
*

Let G be

doi:10.1016/j.disc.2004.10.019
fatcat:5rgbggxtr5cp7ffs5ekhaystli
*a*balanced bipartite*graph*with partite sets X and Y, which has*a**perfect*matching, and let x ∈ X and y ∈ Y . Let k be*a*positive integer. ... Then we prove that if G has k internally disjoint alternating*paths*between x and y with respect to some*perfect*matching, then G has k internally disjoint alternating*paths*between x and y with respect ... For*graph*-theoretic terminology not defined in this*note*, we refer the reader to [2] . In this*note*,*a**path*which starts from*a*vertex x and ends at*a*vertex y is called an xy-*path*. ...##
###
Broder's Chain Is Not Rapidly Mixing
[article]

2014
*
arXiv
*
pre-print

We prove that Broder's Markov chain for approximate sampling near-

arXiv:1404.4249v1
fatcat:t52tnnbmirha3oq3s2z2h6tgxe
*perfect*and*perfect*matchings is not rapidly mixing for Hamiltonian, regular, threshold and planar bipartite*graphs*, filling*a*gap in the ...*graph*is known. ... (*Note*that*a*ladder with 0 rungs has*one**perfect*matching and*a*ladder with 1 rung, too.) We find |N uv (G)| = 6 3k F k+3 . Let us consider the set of*perfect*matchings M (G) in this*graph*. ...##
###
Page 6607 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

Haruo Hosoya (J-OCHS-I; Bunkyo)
97k:05164 05C70
Zhang, Fuji (PRC-XIAM; Xiamen);
Zhang, Heping |Zhang, He Ping*| (PRC-LAN; Lanzhou)

*A**note**on*the number of*perfect*matchings of bipartite*graphs*. ... of the*paths*modulo three, and then choosing (roughly) every third vertex*on*each*path*to form*a*dominating set. ...##
###
Traveling salesman path problems

2006
*
Mathematical programming
*

We first characterize traveling salesman walk

doi:10.1007/s10107-006-0046-8
fatcat:6wa5ktitcrbi3mlt5l7vkwfdcu
*perfect**graphs*,*graphs*for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities. ... The objective is to find*a*minimum cost*path*from the source to destination visiting all cities exactly once. ... Acknowledgements The authors would like to thank Santosh Vempala for suggesting problems*on*traveling salesman*paths*, Kevin Cheung, Michel Goemans, Kunal Talwar Santosh Vempala for many helpful discussions ...##
###
On perfect colorings of infinite multipath graphs
[article]

2020
*
arXiv
*
pre-print

We consider

arXiv:2003.06803v1
fatcat:kzgk5iq5lnef7a6oqfd3dunbku
*a*lexicographic product of the infinite*path**graph*and*a**graph*G that can be either the complete or empty*graph**on*n vertices. ...*A*coloring of vertices of*a*given*graph*is called*perfect*if the color structure of each ball of radius 1 in the*graph*depends only*on*the color of the ball center. Let n be*a*positive integer. ... There is*a**one*-to-*one*correspondence between the*perfect*colorings of an infinite*path**graph*and the block monochrome*perfect*colorings of C ∞ · G; the latter are obtained by G-times copying of the former ...##
###
The computational strength of matchings in countable graphs
[article]

2020
*
arXiv
*
pre-print

In

arXiv:2006.11334v1
fatcat:gnjsgfyngnajbkswztsoua2wdy
*a*1977 paper, Steffens identified an elegant criterion for determining when*a*countable*graph*has*a**perfect*matching. ... The results of this paper explore the relationship between*graph*theory and logic by showing the way in which specific changes to*a*single*graph*-theoretic principle impact the corresponding proof-theoretical ... To see why the new*graph*G , l , r , c has*a*unique*perfect*matching,*note*that in any*perfect*matching, exactly*one*of l or r matches into G • . ...##
###
β-Perfect Graphs

1996
*
Journal of combinatorial theory. Series B (Print)
*

In particular, both referees noticed

doi:10.1006/jctb.1996.0030
fatcat:bkhx6jcbaffyhpmkjeos2t6dai
*a*large hole in an earlier erroneous proof of Theorem 4 and*one*asked about the complexity of determining if*a**graph*is ;-*perfect*. ... Even Holes and ;-*Perfect**Graphs*By*a*hole, we mean an induced subgraph isomorphic to*a*chordless cycle*on*at least four vertices. C k denotes*a*hole*on*k vertices. ... However,*a*;-*perfect**graph*can contain no chordless cycle*on*2k vertices, k 2 (since ;(C 2k )=3 and /(C 2k )=2). ...##
###
Inverses of bipartite graphs

2017
*
Combinatorica
*

In this

doi:10.1007/s00493-016-3502-y
fatcat:4onia7cvabcvjl44osk3gplud4
*note*, we characterize all bipartite*graphs*with*a*unique*perfect*matching whose adjacency matrices have inverses diagonally similar to non-negative matrices, which settles an open problem of Godsil ...*on*inverses of bipartite*graphs*in [Godsil, Inverses of Trees, Combinatorica 5 (1985) 33-39]. ... : If P is an M -alternating*path*, then G\V (P ) has*a**perfect*matching. So G\V (P ) has*a*Sachs subgraph. Now assume that G\V (P ) has*a*Sachs subgraph.*Note*that G\V (P ) is*a*bipartite*graph*. ...
« Previous

*Showing results 1 — 15 out of 125,738 results*