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Page 5877 of Mathematical Reviews Vol. , Issue 2003h
[page]

2003
*
Mathematical Reviews
*

The paper under review studies extensively some chain conditions

*on*families*of*subgroups*of**a*group:*max*-oo and*min*-oo. ... He also studies the structure*of*locally finite groups with*max*-oo or*min*-oo proving that*a*locally finite group G satisfies*max*-oo if and only if it is finite or Priifer-by-finite, and*a*locally finite ...##
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Centers of directed cacti

1989
*
Časopis pro pěstování matematiky
*

The graph G is

doi:10.21136/cpm.1989.118370
fatcat:6qoajwozbnhkjdvkmozoj4enem
*a*strongly connected directed cactus. • The following two*theorems*concern radii*of**cacti*.*Theorem*2. Let k, n be integers, l^Hn-1. ... The following*theorem*shows that the number*of*outcentral vertices in strongly connected directed*cacti*has no upper bound.*Theorem*1. ...##
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Page 6045 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

Jené Lehel (1-LSVL; Louisville, KY)
2000i1:05101 05C35 05B35 90C35
Szigeti, Zoltan (F-PARIS6-CM; Paris)

*On**a**min*-*max**theorem**of**cacti*. ... Summary: “*A*simple proof is presented for the*min*-*max**theorem*05C Graph theory 2000::05106*of*Lovasz*on**cacti*. Instead*of*using the result*of*L. Lovasz [in Al/- gebraic methods in graph theory, Vol. ...##
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Zero forcing number, path cover number, and maximum nullity of cacti

2011
*
Involve. A Journal of Mathematics
*

(

doi:10.2140/involve.2011.4.277
fatcat:esmzd4ikbnfy5ilhm3jyoq5xyi
*A*cactus is*a*graph where each edge is in at most*one*cycle.) MSC2010: primary 05C50; secondary 15A03. ... Results for comparing the parameters are presented, with equality*of*zero forcing number and path cover number shown for all*cacti*and equality*of*zero forcing number and maximum nullity for*a*subset*of*... ZERO FORCING NUMBER, PATH COVER NUMBER, AND MAXIMUM NULLITY*OF**CACTI*291 Then Z(G) = M(G) and n v (G) = 0, but v is not in an optimal zero forcing set for G. ...##
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Sharp upper bounds of $A_\alpha$-spectral radius of cacti with given pendant vertices

2020
*
Hacettepe Journal of Mathematics and Statistics
*

Lastly, without loss

doi:10.15672/hujms.519987
fatcat:4hdmokevwrbznifaowhmeemchm
*of*generality, we consider the case*of**max*{xu1 , xu3 } ≤ xv0 ≤*min*{xv1 , xv3 }, say xu1 ≤ xv0 and xv0 ≤ xv1 . ... Let Cm 2k be the set*of*all 2k-vertex*cacti*with*a*perfect matching.*Theorem*3.5. ...##
###
K-Circular Matroids of Graphs
[article]

2015
*
arXiv
*
pre-print

*A*natural analog (WP)'

*of*Whitney's problem (WP) is to describe the classes

*of*graphs G having the same matroid M'(G), where M'(G) is

*a*matroid (

*on*the edge set

*of*G) distinct from M(G). ... In our next paper we use these results to study

*a*particular problem

*of*(WP)_k

*on*graphs uniquely defined by their k-circular matroids. ... Claim 3.3.5 Let

*A*be

*a*connected graph with at least

*one*cycle. Then Q

*A*has the ⊆-maximum element

*Max*(Q

*A*). Moreover,

*Max*(Q

*A*) =

*Min*(R

*A*) and C is

*a*subgraph

*of*

*A*for every cycle C in

*A*. ...

##
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An $$O(n\log n)$$ O ( n log n ) algorithm for finding edge span of cacti

2015
*
Journal of combinatorial optimization
*

In the paper we study the computational complexity

doi:10.1007/s10878-015-9827-4
fatcat:j5rpvvimozbsrpohrl4gip5fli
*of*the problem*of*finding vertex colorings c*of*G such that: We show that the problem is NP-hard for subcubic outerplanar graphs*of**a*very simple structure ... Next, we use the last two results to construct an algorithm that solves the problem for*a*given cactus G in O(n log n) time, where n is the number*of*vertices*of*G. ... Acknowledgments This project has been partially supported by Narodowe Centrum Nauki under contract DEC-2011/02/*A*/ST6/00201. ...##
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Tight bounds on exploration of constantly connected cacti-paths

2021
*
Zenodo
*

The upper bound is generalized

doi:10.5281/zenodo.5594859
fatcat:ndxlvyd77zdiznejdltuhdrd64
*on*dynamic graphs based*on**cacti*-paths with rings. ... We focus*on*the case where the underlying graph is*a*cactus-path (graph reduced to*a*path*of*rings in which two neighbor rings have at most*one*vertex in common) and we assume that the agent knows the ... Acknowledgments The authors would like to thank David Ilcinkas for insightful and valuable discussions regarding the topic*of*this paper. ...##
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Exploitation of Multiple Replenishing Resources with Uncertainty
[article]

2020
*
arXiv
*
pre-print

core

arXiv:2007.09640v1
fatcat:vveo62wlvra2fadw5bdglhvwva
*of**cacti*. ... We consider an optimization problem in which*a*(single) bat aims to exploit the nectar in*a*set*of*n*cacti*with the objective*of*maximizing the expected total amount*of*nectar it drinks. ... Indeed, the support supp(p * )*of*the optimal strategy p * promised in*Theorem*1.1 and the small core S promised in*Theorem*1.2 consist*of**cacti*i ∈ [n] that admit*a*larger χ i than any*cacti*not included ...##
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Dominating and large induced trees in regular graphs

2007
*
Discrete Mathematics
*

Furthermore, we prove essentially best-possible lower bounds

doi:10.1016/j.disc.2007.03.043
fatcat:45n73srqpnegpoch76kdwzcd5i
*on*the maximum order*of*induced trees in connected*cacti**of*maximum degree 3 and connected cubic graphs. ... Finally, we give*a*forbidden induced subgraph condition for the existence*of*induced dominating trees. ... Instead*of**a*lower bound*on*it(G) for*cacti*G*of*maximum degree at most 3 we will prove*a*slightly stronger result. ...##
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On Split-Coloring Problems

2005
*
Journal of combinatorial optimization
*

First

doi:10.1007/s10878-005-4103-7
fatcat:hwnagh6d45egpkfehypvq25hba
*of*all, we propose the packing problem*of*finding the split graph*of*maximum size where*a*split graph is*a*graph G = (V, E) in which the vertex set V can be partitioned into*a*clique K and*a*stable ... We study*a*new coloring concept which generalizes the classical vertex coloring problem in*a*graph by extending the notion*of*stable sets to split graphs. ...*On*the other hand, any maximum clique*of*G is in the form K*max*∪ {x} where K*max*is*a*maximum clique*of*G and where x ∈ I N . ...##
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Symmetric regular cacti-properties and enumeration

2012
*
Proyecciones
*

We discuss some characteristics

doi:10.4067/s0716-09172012000300006
fatcat:gw3yzkudezhlnlpz2nxigxii5q
*of*symmetric regular*cacti*. The number*of*symmetric regular*cacti**on*given number*of*vertices are also enumerated. ...*A*cactus is*a*connected graph whose all the blocks are isomorphic to cycle or complete graph*on*n vertices. We introduce symmetric regular*cacti*and*a*procedure for their construction. ... The eccentricity*of*the vertex u, written as (u), is*max*{d(u, v) : v ∈ V (G)}. The radius*of**a*graph G, written as rad G, is*min*{ (u) : u ∈ V (G)}. ...##
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On the Atom-Bond Connectivity index of cacti

2014
*
Filomat
*

The Atom-Bond Connectivity (ABC) index

doi:10.2298/fil1408711d
fatcat:m37yqpvnxzfcbpvdabcpqisqei
*of**a*connected graph G is defined as ABC*A*connected graph G is called*a*cactus if any two*of*its cycles have at most*one*common vertex. ... Denote by G 0 (n, r) the set*of**cacti*with n vertices and r cycles and G 1 (n, p) the set*of**cacti*with n vertices and p pendent vertices. ... The neighborhood*of**a*vertex u ∈ V(G) will be denoted by N(u), ∆(G) =*max*{d(u)|u ∈ V(G)} and δ(G) =*min*{d(u)|u ∈ V(G)}. ...##
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On the dominated chromatic number of certain graphs
[article]

2019
*
arXiv
*
pre-print

Let G be

arXiv:1910.02685v1
fatcat:obfa4r7635f2tafuo23itveexi
*a*simple graph. The dominated coloring*of*G is*a*proper coloring*of*G such that each color class is dominated by at least*one*vertex. ... The minimum number*of*colors needed for*a*dominated coloring*of*G is called the dominated chromatic number*of*G, denoted by χ_dom(G). ... So we have*max*{χ dom (G 1 ), χ dom (G 2 )} ≤ χ dom (G 1 ∪ Kr G 2 ).*On*the other hand, first we give colors*a*1 ,*a*2 , . . . ,*a*r to the vertices*of*K r . ...##
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Strong edge-coloring for jellyfish graphs

2015
*
Discrete Mathematics
*

This paper determines strong chromatic indices

doi:10.1016/j.disc.2015.04.031
fatcat:oblyvuckbjdzxgmspuuafcp6la
*of**cacti*, which are graphs whose blocks are cycles or complete graphs*of*two vertices. The proof is by means*of*jellyfish graphs. ... The strong chromatic index*of**a*graph is the minimum number*of*colors used in*a*strong edge-coloring. ... Strong edge-coloring*on**cacti*The purpose*of*this section is to give the strong chromatic indices*of**cacti*. Notice that*a*block-jellyfish*of**a*cactus is either*a*K 2 -jellyfish or*a*C n -jellyfish. ...
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