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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  ... 

Centers of directed cacti

Bohdan Zelinka
1989 Časopis pro pěstování matematiky  
The graph G is 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.  ... 
doi:10.21136/cpm.1989.118370 fatcat:6qoajwozbnhkjdvkmozoj4enem

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.  ... 

Zero forcing number, path cover number, and maximum nullity of cacti

Darren Row
2011 Involve. A Journal of Mathematics  
(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.  ... 
doi:10.2140/involve.2011.4.277 fatcat:esmzd4ikbnfy5ilhm3jyoq5xyi

Sharp upper bounds of $A_\alpha$-spectral radius of cacti with given pendant vertices

Chunxiang WANG, Shaohui WANG, Jia-bao LİU
2020 Hacettepe Journal of Mathematics and Statistics  
Lastly, without loss 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.  ... 
doi:10.15672/hujms.519987 fatcat:4hdmokevwrbznifaowhmeemchm

K-Circular Matroids of Graphs [article]

José F. De Jesús, Alexander Kelmans
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.  ... 
arXiv:1508.05364v1 fatcat:fiiujyobo5bhpecxd2ntc4cqla

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

Robert Janczewski, Krzysztof Turowski
2015 Journal of combinatorial optimization  
In the paper we study the computational complexity 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.  ... 
doi:10.1007/s10878-015-9827-4 fatcat:j5rpvvimozbsrpohrl4gip5fli

Tight bounds on exploration of constantly connected cacti-paths

Ahmed Mouhamadou WADE
2021 Zenodo  
The upper bound is generalized 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.  ... 
doi:10.5281/zenodo.5594859 fatcat:ndxlvyd77zdiznejdltuhdrd64

Exploitation of Multiple Replenishing Resources with Uncertainty [article]

Amos Korman, Yuval Emek, Simon Collet, Aya Goldshtein, Yossi Yovel
2020 arXiv   pre-print
core 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  ... 
arXiv:2007.09640v1 fatcat:vveo62wlvra2fadw5bdglhvwva

Dominating and large induced trees in regular graphs

Dieter Rautenbach
2007 Discrete Mathematics  
Furthermore, we prove essentially best-possible lower bounds 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.  ... 
doi:10.1016/j.disc.2007.03.043 fatcat:45n73srqpnegpoch76kdwzcd5i

On Split-Coloring Problems

T. Ekim, D. de Werra
2005 Journal of combinatorial optimization  
First 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 .  ... 
doi:10.1007/s10878-005-4103-7 fatcat:hwnagh6d45egpkfehypvq25hba

Symmetric regular cacti-properties and enumeration

S. K Vaidya, D. D Bantva
2012 Proyecciones  
We discuss some characteristics 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)}.  ... 
doi:10.4067/s0716-09172012000300006 fatcat:gw3yzkudezhlnlpz2nxigxii5q

On the Atom-Bond Connectivity index of cacti

Hawei Dong, Xiaoxia Wu
2014 Filomat  
The Atom-Bond Connectivity (ABC) index 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)}.  ... 
doi:10.2298/fil1408711d fatcat:m37yqpvnxzfcbpvdabcpqisqei

On the dominated chromatic number of certain graphs [article]

Saeid Alikhani, Mohammad R. Piri
2019 arXiv   pre-print
Let G be 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 .  ... 
arXiv:1910.02685v1 fatcat:obfa4r7635f2tafuo23itveexi

Strong edge-coloring for jellyfish graphs

Gerard J. Chang, Sheng-Hua Chen, Chi-Yun Hsu, Chia-Man Hung, Huei-Ling Lai
2015 Discrete Mathematics  
This paper determines strong chromatic indices 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.  ... 
doi:10.1016/j.disc.2015.04.031 fatcat:oblyvuckbjdzxgmspuuafcp6la
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