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GRAPHS CONTAINING EVERY 2FACTOR
"... Abstract. For a graph G, let σ2(G) = min{d(u) + d(v) : uv / ∈ E(G)}. We prove that every nvertex graph G with σ2(G) ≥ 4n/3−1 contains each 2regular nvertex graph. This extends a theorem due to Aigner and Brandt and to Alon and Fisher. 1. ..."
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Abstract. For a graph G, let σ2(G) = min{d(u) + d(v) : uv / ∈ E(G)}. We prove that every nvertex graph G with σ2(G) ≥ 4n/3−1 contains each 2regular nvertex graph. This extends a theorem due to Aigner and Brandt and to Alon and Fisher. 1.
On (2, t)Choosability of TriangleFree Graphs
, 2013
"... A (k, t)list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and ⋃v∈V(G) L(v)  = t. A graph G is (k, t)choosable if G has a proper coloring f such that f (v) ∈ L(v) for each (k, t)list assignment L. In 2011, Charoenpanitseri, Punnim and Uiyyasathian ..."
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Cited by 1 (1 self)
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proved that every nvertex graph is (2, t)choosable for t ≥ 2n − 3 and every nvertex graph containing a triangle is not (2, t)choosability for t ≤ 2n − 4. Then a complete result on (2, t)choosability of an nvertex graph containing a triangle is revealed. Moreover, they showed that an nvertex
Perfect matching in clawfree cubic graphs
, 2009
"... Abstract Lovász and Plummer conjectured that there exists a fixed positive constant c such that every cubic nvertex graph with no cutedge has at least 2 cn perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove ..."
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Cited by 2 (0 self)
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Abstract Lovász and Plummer conjectured that there exists a fixed positive constant c such that every cubic nvertex graph with no cutedge has at least 2 cn perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove
Exact algorithms for treewidth and minimum fillin
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP 2004). Lecture Notes in Comput. Sci
, 2004
"... We show that the treewidth and the minimum fillin of an nvertex graph can be computed in time O(1.8899 n). Our results are based on combinatorial proofs that an nvertex graph has O(1.7087 n) minimal separators and O(1.8135 n) potential maximal cliques. We also show that for the class of ATfree g ..."
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Cited by 28 (17 self)
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We show that the treewidth and the minimum fillin of an nvertex graph can be computed in time O(1.8899 n). Our results are based on combinatorial proofs that an nvertex graph has O(1.7087 n) minimal separators and O(1.8135 n) potential maximal cliques. We also show that for the class of AT
vices. Monotone Circuits for Matching Require Linear Depth
, 2003
"... We prove that monotone circuits computing the perfect matching function on nvertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
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We prove that monotone circuits computing the perfect matching function on nvertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.
On domination in connected cubic graphs
, 2005
"... In 1996, Reed proved that the domination number γ(G) of every nvertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that γ(H)�⌈n/3 ⌉ for every connected 3regular (cubic) nvertex graph H. In this note, we disprove this conjecture. We construct a connected cubic graph ..."
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Cited by 6 (2 self)
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In 1996, Reed proved that the domination number γ(G) of every nvertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that γ(H)�⌈n/3 ⌉ for every connected 3regular (cubic) nvertex graph H. In this note, we disprove this conjecture. We construct a connected cubic
Oretype graph packing problems
, 2006
"... We say that nvertex graphs G1,G2,...,Gk pack if there exist injective mappings of their vertex sets onto [n] ={1,...,n} such that the images of the edge sets do not intersect. The notion of packing allows one to make some problems on graphs more natural or more general. Clearly, two nvertex graphs ..."
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Cited by 8 (5 self)
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We say that nvertex graphs G1,G2,...,Gk pack if there exist injective mappings of their vertex sets onto [n] ={1,...,n} such that the images of the edge sets do not intersect. The notion of packing allows one to make some problems on graphs more natural or more general. Clearly, two nvertex
Circumference of Graphs with Bounded Degree
"... Karger, Motwani and Ramkumar have shown that there is no constant approximation algorithm to find a longest cycle in a Hamiltonian graph, and they conjectured this is the case even for graphs with bounded degree. On the other hand,Feder, Motwani and Subi have shown that there is a polynomial time a ..."
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Cited by 5 (2 self)
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algorithm for finding a cycle of length nlog3 2 in a 3connected cubic nvertex graph. In this paper,we show that if G is a 3connected nvertex graph with maximum degree at most d, then one can find, in O(n3) time, a cycle in G of length at least \Omega (nlogb 2), where b = 2(d 1)² + 1.
A better bound for the cop number of general graphs
 Journal of Graph Theory
, 2008
"... Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to ..."
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Cited by 22 (2 self)
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Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to
The worstcase time complexity for generating all maximal cliques, COCOON
 Lecture Notes in Computer Science,
, 2004
"... Abstract We present a depthfirst search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in the BronKerbosch algorithm. All the maximal cliques generated are output in a treelike form. Subsequently, we prove that its worstcase time co ..."
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Cited by 82 (1 self)
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complexity is O(3 n/3 ) for an nvertex graph. This is optimal as a function of n, since there exist up to 3 n/3 maximal cliques in an nvertex graph. The algorithm is also demonstrated to run very fast in practice by computational experiments.
Results 11  20
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3,569