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

##
###
The vertex (edge) independence number, vertex (edge) cover number and the least eigenvalue of a graph

2010
*
Linear Algebra and its Applications
*

among all graphs

doi:10.1016/j.laa.2010.04.009
fatcat:ymj6l6be7ravrlaryabgdth74a
*of*a fixed*order*and a given vertex (*edge*) independence*number*or vertex (*edge*)*cover**number*, and get some bounds for*the*vertex (*edge*) independence*number*, vertex (*edge*)*cover**number*... Keywords: Graph Adjacency matrix Vertex (*edge*) independence*number*Vertex (*edge*)*cover**number*Least eigenvalue In this paper we characterize*the*unique graph whose least eigenvalue attains*the*minimum ...*The*vertex (*edge*) independence*number**of*G, denoted by α(G) (α (G)), is*the*maximum*of**the*cardinalities*of*all vertex (*edge*) independent*sets*. • A vertex (*edge*)*cover**of*a graph G is a*set**of*vertices ...##
###
On intersecting hypergraphs

1998
*
Discrete Mathematics
*

We investigate

doi:10.1016/s0012-365x(97)00136-2
fatcat:segaq44abjb65mzojpn4xgafda
*the*following question: 'Given an intersecting multi-hypergraph on n points, what fraction*of**edges*must be*covered*by any*of**the*best 2 points?' ... To better study this problem, we introduce*the*concept*of*fractional matchings and*coverings**of**order*2. ...*The**set**of**edges**covered*by a vertex v is*the**set*{X E E(H): vEX}, and*the**set**of**edges**covered*by a*set**of*vertices is*the*union*of**the**sets**covered*by each vertex. ...##
###
Some remarks on normalized matching

1983
*
Journal of combinatorial theory. Series A
*

To obtain (3), we discuss "minimal

doi:10.1016/0097-3165(83)90015-8
fatcat:dkvc62tkc5dnxblxeptopecdl4
*sets*"*of**covering*relations between two adjacent levels*of*an LYM-*order*. ... Then (XC [n]: ai < lXnA,l <b,},*ordered*by inclusion, is a poset having*the*LYM property. (2)*The*smallest regular*covering**of*an LYM*order*has M(P) chains, where M(P) is*the*least common multiple*of**the*... Similarly,*the**order*on*the**edges*from x induces a*set*B*of*partial sums for*the*flow multiplicites. Note that 1 B 1 is*the**number**of*elements*covering*x. ...##
###
The elimination procedure for the competition number is not optimal

2006
*
Discrete Applied Mathematics
*

Given an acyclic digraph D,

doi:10.1016/j.dam.2005.11.009
fatcat:z4dpj7eac5gcreghdq6iolhrea
*the*competition graph C(D) is defined to be*the*undirected graph with V (D) as its vertex*set*and where vertices x and y are adjacent if there exists another vertex z such that ...*the*competition*number*for all graphs. ... Acknowledgments*The*author would like to thank Fred Roberts and Suh-Ryung Kim for helpful discussions and encouragement and an anonymous referee for suggestions that improved*the*readability*of**the*paper ...##
###
Inversions, cuts, and orientations

1991
*
Discrete Mathematics
*

Let P be an n-element

doi:10.1016/0012-365x(91)90045-4
fatcat:lya4w7aykbb7xlk63wh3r7fv6y
*ordered**set*with connected*covering*graph. Then*the**number**of*distinct inversions is at least (n' + 2n)/2 -n log, n. ... Let e(n) be*the*smallest*number*such that any inversion*of*P can be produced by pushdowns reversing successively at most e(n)*edges*.*ordered**set*? ...##
###
Series-parallel planar ordered sets have pagenumber two
[chapter]

1997
*
Lecture Notes in Computer Science
*

We say a

doi:10.1007/3-540-62495-3_34
fatcat:f6ml5fpxireszje4wl7nivtbom
*covers*b (or b*covered*by a) in*the**ordered**set*P, and write a ~ b (or b -< a), if whenever a > c > b then c = b. ... In a book embedding for an*ordered**set*P*the*vertices*of*P on*the*spine form a linear extension (a total*order*L = {xl < x2 < ' . . < x~}*of**the*elements*of*P is a linear extension if x < y in L whenever ... Also, they derive a general lower bound on*the*page*number**of**ordered**sets*and upper bounds for special classes*of**ordered**sets*. ...##
###
Enumerating orientations of ordered sets

1991
*
Discrete Mathematics
*

We exploit independent subsets and matchings to establish further such estimates for certain

doi:10.1016/0012-365x(91)90012-q
fatcat:s3h2drqi5rcrzfic67fcz6crlm
*of**the*outstanding classes*of**ordered**sets*. ... Rival, Enumerating orientations*of**ordered**sets*, Discrete Mathematics 88 (1991) 239-247. Almost every connected, n-element*ordered**set*has 2"" orientations. ... Moreover, we thank one referee for pointing out to use*the*formulation, especially*of*Theorem 6, more general than our original one. ...##
###
Generalized abc-Block Edge Transformation Graph Q

2019
*
Zenodo
*

A cut vertex

doi:10.5281/zenodo.3203811
fatcat:the2jbklvrhsvhkseyn6l3wmja
*of*a connected graph is*the*one whose removal increases*the**number**of*components. ... Throughout*the*paper, we only consider simple graphs without isolated vertices. Definitions not given here may be found in [5]. ...*The*vertex*covering**number*α 0 (G)*of*G is*the*minimum*number**of*vertices in a vertex*covering**set**of*G. A*set**of**edges*in a graph G is an*edge**covering**set*, which*covers*all vertices*of*G. ...##
###
Signed (b,k)-Edge Covers in Graphs

2010
*
Intelligent Information Management
*

Let be a simple graph with vertex

doi:10.4236/iim.2010.22017
fatcat:nbfbrfxwmrbbtela3api354uca
*set*and*edge**set*. Let have at least vertices*of*degree at least , where and b are positive integers. A function is said to be a signed -*edge**cover**of*G if ( , b k) ... For an excellent survey*of*results on*edge**covers*and b-*edge**covers*, see Schrijver [5] . We consider a variant*of**the*standard*edge**cover*problem. Let G be a graph with vertex*set*and*edge**set*. ... A b-*edge**cover**of*a graph G is a*set*C*of**edges**of*G such that each vertex*of*G is incident to at least b*edges**of*C. ...##
###
Nonsplit Geodetic Number of a Lict Graph

2014
*
International Journal of Computer Applications
*

*The*bounds on non split geodetic

*number*in terms

*of*elements

*of*G and

*covering*

*number*

*of*G. Further

*the*relationship between nonsplit geodetic

*number*and geodetic

*number*

*of*a graph is established. ... is a geodetic

*set*and S V is connected.

*The*nonsplit geodetic

*number*

*of*a lict graph G , denoted by G g ns , is

*the*minimum cardinality

*of*a nonsplit geodetic

*set*

*of* G . ...

*The*

*edge*

*covering*

*number* G 1

*of*a graph G is

*the*minimum cardinality

*of*an

*edge*

*cover*

*of*G. ...

##
###
The geodetic vertex covering number of a graph

2020
*
Malaya Journal of Matematik
*

*The*minimum cardinality

*of*a geodetic vertex

*cover*is

*the*geodetic vertex

*covering*

*number*

*of*G denoted by g α (G). Any geodetic vertex

*cover*

*of*cardinality g α (G) is a g α -

*set*

*of*G. ... A subset S

*of*vertices in a connected graph G

*of*

*order*at least two is called a geodetic vertex

*cover*if S is both a geodetic

*set*and a vertex

*covering*

*set*. ...

*The*vertex

*covering*

*number*

*of*a graph was studied in [7] . A

*set*

*of*vertices (

*edges*) in a graph G is independent if no two

*of*

*the*vertices (

*edges*) are adjacent. ...

##
###
The Covert Set-Cover Problem with Application to Network Discovery
[chapter]

2010
*
Lecture Notes in Computer Science
*

We want to find a small

doi:10.1007/978-3-642-11440-3_21
fatcat:wjkj3sdg4zdppjpcw6rdspusau
*set*-*cover*using a minimal*number**of*such queries. ... We apply this technique to*the*network discovery problem that involves certifying all*the**edges*and non-*edges**of*an unknown n-vertices graph based on layered-graph queries from a minimal*number**of*vertices ... Acknowledgement*The*first author is thankful to Rajeev Raman and Thomas Erlebach for introducing him to*the*problem and subsequent technical discussions. ...##
###
On total covering and matching of graphs

1978
*
Journal of combinatorial theory. Series B (Print)
*

Let G be a graph with no loops or multiple

doi:10.1016/0095-8956(78)90017-5
fatcat:rgieppoz5ndx5mpdbokefz2hsu
*edges*having node*set*N(G) and*edge**set*E(G).*The*elements*of*N(G) u E(G) are called elements*of*G. ... Two elements*of*G are called independent if neither one*covers**the*other. A*set*%*of*elements*of*G is called a total*cover*if*the*elements*of*%Y*cover*all elements*of*G and V is minimal. ... Because*of**the*assumed minimality*of**the**number**of**edges*in 4,*the*node Q must be joined to a node S and S E 9. ...##
###
Fractional Biclique Covers and Partitions of Graphs

2006
*
Electronic Journal of Combinatorics
*

This paper investigates

doi:10.37236/1100
fatcat:4edzt2pcq5ekhe42zzupndtafy
*the*fractional biclique*cover**number*, $bc^*(G)$, and*the*fractional biclique partition*number*, $bp^*(G)$,*of*a graph $G$. ... It is also shown that $bc^*(G)$ is a better lower bound on*the*Boolean rank*of*a binary matrix than*the*maximum*number**of*isolated ones*of**the*matrix. ... Gregory for mentioning*the*definition*of*bp * (G), observing that*edges*in*the*same orbit*of*Aut G may be assigned*the*same weight, and for suggesting Theorem 3.2. ...##
###
A Generalization of Opsut's Lower Bounds for the Competition Number of a Graph

2012
*
Graphs and Combinatorics
*

*The*competition graph C(D)

*of*a digraph D is a (simple undirected) graph which has

*the*same vertex

*set*as D and has an

*edge*between two distinct vertices x and y if and only if there exists a vertex v ... Roberts defined

*the*competition

*number*k(G)

*of*a graph G as

*the*minimum

*number*

*of*such isolated vertices. ... Acknowledgment

*The*author was supported by JSPS Research Fellowships for Young Scientists.

*The*author was also supported partly by Global COE program "Fostering Top Leaders in Mathematics". ...

« Previous

*Showing results 1 — 15 out of 966,878 results*