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Perfect Matchings in Clawfree Cubic Graphs
, 2009
"... Lovász and Plummer conjectured that there exist 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 that every ..."
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Cited by 2 (0 self)
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Lovász and Plummer conjectured that there exist 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 that every
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
Published by Canadian Center of Science and Education On (2, t)Choosability of TriangleFree Graphs
"... 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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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
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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Cited by 1 (0 self)
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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.
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
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
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.
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
Results 11  20
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181,387