A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Cubic graphs with equal independence number and matching number
[article]

2019
*
arXiv
*
pre-print

Caro, Davila,

arXiv:1910.11762v1
fatcat:zoepwm2yxbforov2i3654dw6lq
*and*Pepper (arXiv:1909.09093) recently proved δ(G) α(G)≤Δ(G) μ(G) for every*graph*G*with*minimum degree δ(G), maximum degree Δ(G),*independence**number*α(G),*and**matching**number*μ(G). ... Answering some problems they posed, we characterize the extremal*graphs*for δ(G)<Δ(G) as well as for δ(G)=Δ(G)=3. ... Acknowledgment We thank Yair Caro, Randy Davila,*and*Ryan Pepper for valuable discussion*and*for sharing their many crucial examples of extremal*graphs*. ...##
###
On the maximum number of independent edges in cubic graphs

1982
*
Discrete Mathematics
*

Given an extended real

doi:10.1016/0012-365x(82)90227-8
fatcat:qbuy5aaecnfsllzyo33maeklzu
*number*r, a property P(r) of*graphs*is super-hereditary if, whenever*graph*G has property P(r)*and*H is a subgraph of G, then H has property P(s)*with*s I> r. ... Let the reals be extended to include oo*with*o~ > r for every real nuraber r. ... is a*cubic**graph**with*n vertices*and*property P, then G contains a*matching**with*at least ½n(3g-1)/(3g-~-1) edges. ...##
###
Page 1494 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

We provide a constructive characterisation of those trees

*with**equal*domination*and*restrained domination*numbers*. ... Summary: “It is known that finding a perfect*matching*in a general*graph*is AC’-equivalent to finding a perfect*matching*in a 3-regular (i.e.*cubic*)*graph*. ...##
###
Matchings and Nonrainbow Colorings

2009
*
SIAM Journal on Discrete Mathematics
*

We show that the maximum

doi:10.1137/060675927
fatcat:oijob43zdfgvja5h23cg7anu2i
*number*of colors that can be used in a vertex coloring of a*cubic*3-connected plane*graph*G that avoids a face*with*vertices of mutually distinct colors (a rainbow face) is*equal*... to n 2 + µ * − 2, where n is the*number*of vertices of G*and*µ * is the size of the maximum*matching*of the dual*graph*G * . ... In particular, n 2 + μ * − 2 ≤ χ f (G) ≤ n − α * for connected*cubic*plane*graphs*G [10] , where α * is the*independence**number*of the dual*graph*G * of G*and*μ * is the size of the largest*matching*of ...##
###
Average connectivity and average edge-connectivity in graphs

2013
*
Discrete Mathematics
*

In this paper, we prove a relationship between the average connectivity

doi:10.1016/j.disc.2013.05.024
fatcat:watglpdtynbprf3fdrnjqdvvgy
*and*the*matching**number*in all*graphs*. ... We also give the best lower bound for the average edge-connectivity over n-vertex connected*cubic**graphs*,*and*we characterize the*graphs*where*equality*holds. ... We will show that*equality*holds only*graphs*in a family. The family is also useful to find the minimum*number*of perfect*matchings*over n-vertex*cubic**graphs*having a perfect*matching*. ...##
###
CLIQUE-TRANSVERSAL SETS IN LINE GRAPHS OF CUBIC GRAPHS AND TRIANGLE-FREE GRAPHS

2015
*
Bulletin of the Korean Mathematical Society
*

For every

doi:10.4134/bkms.2015.52.5.1423
fatcat:bcp67yza4ncmlcluvdopk5sscm
*cubic**graph**with*at most two bridges, we first show that it has a perfect*matching*which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal ... Also, we present a sharp upper bound on the cliquetransversal*number*of line*graph*of a*cubic**graph*. ... If G is a*cubic**graph*of order n*with*girth r ≥ 3, then α ′ (G) ≥ 3g−1 3g+1 n 2 , where g is the*number*of vertices in B. Moreover, the*equality*holds if*and*only if G is the*graph*H(g). holds. ...##
###
Zero Forcing in Claw-Free Cubic Graphs
[article]

2018
*
arXiv
*
pre-print

In this paper we show a surprising relation between the zero forcing

arXiv:1802.03108v1
fatcat:vyrdfeghtrecbftggmnmelopfu
*number*of a*graph**and*the*independence**number*of a*graph*, denoted α(G). ... As a consequence of this result, if G K_4 is a connected,*cubic*, claw-free*graph**with*order n, then Z(G) <2/5n + 1. ... First to establish a relationship between the zero forcing*number*of a*cubic*, claw-free*graph**and*its*independence**and**matching**numbers*. ...##
###
Domination number of cubic graphs with large girth
[article]

2009
*
arXiv
*
pre-print

We show that every n-vertex

arXiv:0907.1166v1
fatcat:seycafb2ifcydbnyzc7qhldmee
*cubic**graph**with*girth at least g have domination*number*at most 0.299871n+O(n/g)<3n/10+O(n/g). ... The authors would like to thank RisteŠkrekovski who was hosting them for an extra-ordinary working conditions*and*for numerous discussions on the subject. ... Fix a*cubic*bridgeless*graph*G*with*girth at least g*and*also fix an integer K which determines the*number*of levels as defined later. ...##
###
Subgroup sum graphs of finite abelian groups
[article]

2021
*
arXiv
*
pre-print

We study perfectness, clique

arXiv:2111.05748v1
fatcat:xlfssinwdjaq7e5kjoo32fapie
*number**and**independence**number*, connectedness, diameter, spectrum,*and*domination*number*of these*graphs**and*their complements. ... The subgroup sum*graph*Γ_G,H is the*graph**with*vertex set G, in which two distinct vertices x*and*y are joined if x+y∈ H∖{0}. These*graphs*form a fairly large class of Cayley sum*graphs*. ... Tamizh Chelvam is supported by CSIR Emeritus Scientist Scheme (No.21 (1123)/20/EMR-II) of Council of Scientific*and*Industrial Research, Government of India. ...##
###
More on the sixth coefficient of the matching polynomial in regular graphs
[article]

2017
*
arXiv
*
pre-print

We find the sixth coefficient of the

arXiv:1710.07426v1
fatcat:pshlnxywwjdhtpubbo7s7kjyoy
*matching*polynomial of regular*graphs*. As a consequence, every*cubic**graph*of order 10 is*matching*unique. ... A*matching*set M in a*graph*G is a collection of edges of G such that no two edges from M share a vertex. In this paper we consider some parameters related to the*matching*of regular*graphs*. ... In the next section, after investigation of the saturation*number**and*the*matching**number*of*cubic**graphs*of order 10, we establish a formula for the*number*of 5-*matchings*in regular*graphs*. ...##
###
Domination number of cubic graphs with large girth

2011
*
Journal of Graph Theory
*

We show that every n-vertex

doi:10.1002/jgt.20568
fatcat:js2s7iiwhrfvhbtuflk4dgyykq
*cubic**graph**with*girth at least g have domination*number*at most 0.299871n + O (n/g) < 3n/10 + O (n/g). ... The authors would like to thank RisteŠkrekovski who was hosting them for an extra-ordinary working conditions*and*for numerous discussions on the subject. ... [2] for bridgeless n-vertex*cubic**graphs**with*girth at least g for g divisible by three*and*1 3 + 8 3g 2 n of Kostochka*and*Stodolsky [5] for all n-vertex*cubic**graphs**with*girth at least g. ...##
###
Domination in Cubic Graphs of Large Girth
[chapter]

2008
*
Lecture Notes in Computer Science
*

We prove that connected

doi:10.1007/978-3-540-89550-3_20
fatcat:5p3djeq36vdfjfg4k5pxfocg4m
*cubic**graphs*of order n*and*girth g have domination*number*at most 0.32127n + O n g . ... Since for fixed d*and*g the*numbers*of cycles in random*cubic**graphs*of fixed lengths r < g are asymptotically distributed as*independent*Poisson variables [2]*with*mean (d − 1) r /2r, the*number*of ... Let H denote the*graph**with*vertex set V \ D 0 whose edges are the edges of the paths in P together*with*the*matching*M . Note that M is a perfect*matching*of H. ...##
###
Perfect matchings of line graphs with small maximum degree
[article]

2009
*
arXiv
*
pre-print

As a corollary, we prove that the

arXiv:0906.3873v1
fatcat:muf5uellzbgxxe4kfbbb7g7nv4
*number*of perfect*matchings*of a connected*cubic*line*graph**with*n vertices*equals*2^n/6+1 if n>4, which implies the conjecture by Lovász*and*Plummer holds for the connected ... We show that if G has an even*number*of edges, then the*number*of perfect*matchings*of the line*graph*of G*equals*2^n/2+1, where n is the*number*of 3-degree vertices of G. ... As a corollary, we also prove that the*number*of perfect*matchings*of a connected*cubic*line*graph**with*n vertices*equals*2 n/6+1 if n > 4. ...##
###
Largest 2-regular subgraphs in 3-regular graphs
[article]

2019
*
arXiv
*
pre-print

For a

arXiv:1903.08795v1
fatcat:bciesaaemrcl5h3gdyost7p6t4
*graph*G, let f_2(G) denote the largest*number*of vertices in a 2-regular subgraph of G. We determine the minimum of f_2(G) over 3-regular n-vertex simple*graphs*G. ... More generally, every n-vertex multigraph*with*maximum degree 3*and*m edges has a 2-regular subgraph that omits at most {0, (3n-2m+c-1)/2} vertices. ... Since O*and*West [9] showed that a*cubic*n-vertex*graph*has at most (n − 7)/3 cut-edges, Theorem 1.1 immediately yields a lower bound on f 2 (G) for a*cubic**graph*G in terms of the*number*of vertices ...##
###
Minimum maximal matchings in cubic graphs
[article]

2021
*
arXiv
*
pre-print

We prove that every connected

arXiv:2008.01863v3
fatcat:o6t5qszo3fakpedk3dwkaolfi4
*cubic**graph**with*n vertices has a maximal*matching*of size at most 5/12 n+ 1/2. ... More generally, we prove that every*graph**with*n vertices*and*m edges*and*maximum degree at most 3 has a maximal*matching*of size at most 4n-m/6+ 1/2. ... The author thanks the two anonymous reviewers for their detailed comments*and*suggestions. ...
« Previous

*Showing results 1 — 15 out of 35,027 results*