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### More sufficient conditions for a graph to have factors

R.P. Anstee, Yunsun Nam
1998 Discrete Mathematics
(g, f)-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

Man Liu, Qingzhi Yu, Shuling Wang, Changhua Huang
2012 Applied Mathematics
Favaron popularized 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.  ...

### A Note on Polynomials and $f$-Factors of Graphs

Hamed Shirazi, Jacques Verstraëte
2008 Electronic Journal of Combinatorics
Lovász defines an $f$-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

Michael D. Plummer
2007 Discrete Mathematics
In the most general sense, 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

Gary Chartrand, Albert D. Polimeni, M. James Stewart
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

Ashwin Ganesan
2013 Wireless networks
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  ...  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]

Jie Han, Yoshiharu Kohayakawa, Patrick Morris, Yury Person
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]

Ashwin Ganesan
2009 arXiv   pre-print
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  ...  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

Ashwin Ganesan
2019 Figshare
Row constraints are known 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

Wei Gao, Yun Gao
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]

Hongliang Lu
2012 arXiv   pre-print
Let 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]

Stefan Glock and Daniela Kühn and Deryk Osthus
2021 arXiv   pre-print
We survey recent advances in the theory of 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]

Peng Wang, Baowen Xu
2009 Lecture Notes in Computer Science
Structure-based methods are 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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