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More sufficient conditions for a graph to have factors

1998
*
Discrete Mathematics
*

(g, f)-

doi:10.1016/s0012-365x(97)00158-1
fatcat:4w52v36ptjdrlnqznmbs3yeruy
*factors*) of*a*given*graph*using fractional subgraphs as*a*basis. These fractional subgraphs are often easy*to*obtain by heuristics. ... We apply our results*to*generalize results of Kano, Bermond and Las Vergnas among others and extend the possibilities*for*included (or forced) edges and excluded edges. ~) ... Using l>~1, (3) and (4) Thus given k, l,*a*, b we can give degree*Conditions*on G*sufficient**to*give the desired (g, f )-*factor*. An attractive special case is the following. Proposition 3.3. ...##
###
Some Results on (1,2n – 1)-Odd Factors

2012
*
Applied Mathematics
*

Favaron popularized

doi:10.4236/am.2012.312255
fatcat:r5fwitjzkfdw3dvqng5dm42zgy
*a*series of the properties of perfect matching*to*k-*factor*critical, at the same time the*sufficient*and necessary*conditions*were given*for*the*graph**to*be k-*factor*critical,*more*... The*sufficient*and necessary*condition**for**graph**to**have*f -odd*factor*was given in paper [1] Ryjacek [2] introduced one kind of new closure operation: let be*a**graph*, G x V G x , if the subgraph ... Then 1 2 , , which is contradiction*to*the fact that x is*a*locally connected vertex, since k The proof is complete. ...##
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A Note on Polynomials and $f$-Factors of Graphs

2008
*
Electronic Journal of Combinatorics
*

Lovász defines an $f$-

doi:10.37236/897
fatcat:5rvxcy62afdldnvsa2k4whwri4
*factor*of $G$*to*be*a*spanning subgraph $H$ of $G$ in which $d_{H}(v) \in f(v)$*for*all $v \in V$. ... Let $G = (V,E)$ be*a**graph*, and let $f : V \rightarrow 2^{\Bbb Z}$ be*a*function assigning*to*each $v \in V$*a*set of integers in $\{0,1,2,\dots,d(v)\}$, where $d(v)$ denotes the degree of $v$ in $G$. ... Our next result is*a**sufficient**condition**for**a**graph**to**have**a*partial f -*factor*: Theorem 2 Let G = (V, E) be*a**graph*, and let f satisfy |E| > v∈V |f (v) c \{0}| where f (v) c = {0, 1, 2, . . . , d(v) ...##
###
Graph factors and factorization: 1985–2003: A survey

2007
*
Discrete Mathematics
*

In the most general sense,

doi:10.1016/j.disc.2005.11.059
fatcat:fdvo3uo72fhjrpybbdbgtkm2gy
*a**factor*of*a**graph*G is just*a*spanning subgraph of G and*a**graph**factorization*of G is*a*partition of the edges of G into*factors*. ... However, as we shall see in the present paper, even this extremely general definition does not capture all the*factor*and*factorization*problems that*have*been studied in*graph*theory. ... The author is also grateful*to*the referees*for*their constructive comments. ...##
###
The existence of 1-factors in line graphs, squares, and total graphs

1973
*
Indagationes Mathematicae (Proceedings)
*

*For*

*a*connected

*graph*B, it is shown that

*a*necessary and

*sufficient*

*condition*that L(B) (respectively, Q*; respectively, T(Q))

*have*

*a*l-

*factor*is that L(U) (respectively, Ga; respectively, T(G))

*have*...

*A*l-

*factor*of

*a*

*graph*is

*a*spanning l-regular subgraph. ... The object of this paper is

*to*give

*a*necessary and

*sufficient*

*condition*

*for*each of the

*graphs*L(G), Gz, and T(G),

*for*

*a*

*graph*0,

*to*possess

*a*l-

*factor*. ...

##
###
Performance of sufficient conditions for distributed quality-of-service support in wireless networks

2013
*
Wireless networks
*

Given

doi:10.1007/s11276-013-0680-z
fatcat:febta35qhvawfdd2rbf2qqttoi
*a*wireless network where some pairs of communication links interfere with each other, we study*sufficient**conditions**for*determining whether*a*given set of minimum bandwidth quality-of-service (QoS ... The interference in the network is modeled using*a*conflict*graph*whose vertices correspond*to*the communication links in the network. ... Acknowledgements Thanks are due*to*professor Parmesh Ramanathan*for*suggesting this direction of scaling the*sufficient**conditions*. ...##
###
Clique-factors in sparse pseudorandom graphs
[article]

2018
*
arXiv
*
pre-print

*a*K_t-

*factor*, that is, vertex-disjoint copies of K_t covering every vertex of G. ... We prove that

*for*any t> 3 there exist constants c>0 and n_0 such that any d-regular n-vertex

*graph*G with t| n≥ n_0 and second largest eigenvalue in absolute value λ satisfying λ< c d^t/n^t-1 contains ... It is straightforward

*to*generalize Theorem 1.2

*to*K t -

*factors*and (εp t n, p)-bijumbled

*graphs*with minimum degree pn 2 and ε = ε t > 0

*sufficiently*small.

*A*

*condition*

*for*arbitrary 2-

*factors*. ...

##
###
On some sufficient conditions for distributed Quality-of-Service support in wireless networks
[article]

2009
*
arXiv
*
pre-print

Given

arXiv:0906.3782v1
fatcat:h5ctk44v5bf33irmxfy6rhi5vu
*a*wireless network where some pairs of communication links interfere with each other, we study*sufficient**conditions**for*determining whether*a*given set of minimum bandwidth Quality of Service (QoS ... These algorithms are seen*to*be within*a*bounded*factor*away from optimal*for*some well known classes of networks and interference models. ... ACKNOWLEDGEMENTS Thanks are due*to*professor Parmesh Ramanathan*for*suggesting this direction of scaling the*sufficient**conditions*. ...##
###
On some sufficient conditions for distributed QoS support in wireless networks

2019
*
Figshare
*

Row constraints are known

doi:10.6084/m9.figshare.8253194.v1
fatcat:lbjrwe55lzgmzi4nl47php7g6u
*to*be*sufficient*, and we introduce the notion of the induced star number of*a**graph*and show that this quantity determines the performance of this*condition*. ... Given*a*wireless network where some pairs of communication links interfere with each other, we study*sufficient**conditions**for*determining whether*a*given set of minimum bandwidth Quality of Service (QoS ... Acknowledgements Thanks are due*to*professor Parmesh Ramanathan*for*suggesting this direction of scaling the*sufficient**conditions*. ...##
###
Page 9591 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

In this paper, we give

*a*necessary and*sufficient**condition**for**a*bipartite*graph**to**have*an f-*factor*containing*a*set of edges and excluding another set of edges and discuss some applications of this ... In particular, we obtain some suffi- cient*conditions*related*to*connectivity and edge-connectivity*for**a*bipartite (m/f )-*graph**to**have*an f-*factor*with special properties and generalize the results in ...##
###
Toughness Condition for a Graph to Be a Fractional(g,f,n)-Critical Deleted Graph

2014
*
The Scientific World Journal
*

*A*graphGis called

*a*fractional(g,f)-deleted

*graph*ifG-{e}admits

*a*fractional(g,f)-

*factor*

*for*anye∈E(G). ...

*A*graphGis called

*a*fractional(g,f,n)-critical deleted

*graph*if, after deleting anynvertices fromG, the resulting

*graph*is still

*a*fractional(g,f)-deleted

*graph*. ... They also would like

*to*thank the anonymous referees

*for*providing them with constructive comments and suggestions. ...

##
###
Simplified existence theorems on all fractional [a,b]-factors
[article]

2012
*
arXiv
*
pre-print

Let

arXiv:1103.3983v2
fatcat:ztgy4jbarzes7eo7sfu4zeuohi
*a*<b be two positive integers.*sufficiently*large all fractional (g,f)-*factors*, then we say that G has all fractional [*a*,b]-*factors*. Suppose that n is*sufficiently*large*for**a*and b. ... Let G be*a**graph*with order n and let g, f : V (G)→ N such that g(v)≤ f(v)*for*all v∈ V(G). ... Niessen [8] obtained*a*necessary and*sufficient**condition**for**a**graph**to**have*all (g, f )-*factors*. ...##
###
Extremal aspects of graph and hypergraph decomposition problems
[article]

2021
*
arXiv
*
pre-print

We survey recent advances in the theory of

arXiv:2008.00926v3
fatcat:6ijnryj3l5g6lmjkv5ic6qsc54
*graph*and hypergraph decompositions, with*a*focus on extremal results involving minimum degree*conditions*. ... We also collect*a*number of intriguing open problems, and formulate new ones. ... We say that*a**graph*G is F -divisible if e(F ) | e(G) and gcd(F ) | gcd(G). It is easy*to*see that*a*necessary*condition**for*G*to**have*an F -decomposition is*to*be F -divisible. ...##
###
An Effective Similarity Propagation Method for Matching Ontologies without Sufficient or Regular Linguistic Information
[chapter]

2009
*
Lecture Notes in Computer Science
*

Structure-based methods are

doi:10.1007/978-3-642-10871-6_8
fatcat:mv5rxchtengqdfkpcfsmairkry
*more*practical*for*this situation. Similarity propagation is*a*feasible idea*to*realize the structure-based matching. ... This method has two features: (1) It has*more*strict but reasonable propagation*conditions*which make matching process become*more*efficient and alignments become better. (2)*A*series of propagation strategies ...*For*example, when we try*to*use the*graph*matching API provided by SOQA − SimP ack [6]*to*match ontology*graphs*, we find it needs*more*than several days or even several weeks*for**a*normal matching task ...##
###
Page 4450 of Mathematical Reviews Vol. , Issue 84k
[page]

1984
*
Mathematical Reviews
*

Bankfalvi [Theory of

*graphs*(Tihany, 1966), 11-18, Academic Press, New York, 1968; MR 38 #2052] and states necessary and*sufficient**conditions**for*K,*to**have**a*Hamiltonian circuit in which red and blue ... The authors establish necessary and*sufficient**conditions**for*K,,*to**have**a*subgraph in which », is incident with exactly f, red edges and f, blue COMBINATORICS 4450 edges*for*i=1,---,nm. ...
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