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Collapsible biclawfree graphs
, 2006
"... A graph is called biclawfree if it has no biclaw as an induced subgraph. In this note, we prove that if G is a connected bipartite biclawfree graph with δ(G) ≥ 5, then G is collapsible, and of course supereulerian. This bound is best possible. 1 ..."
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A graph is called biclawfree if it has no biclaw as an induced subgraph. In this note, we prove that if G is a connected bipartite biclawfree graph with δ(G) ≥ 5, then G is collapsible, and of course supereulerian. This bound is best possible. 1
Erratum Erratum to “Collapsible biclawfree graphs” [Discrete Math. 306 (2006) 2115–2117]
, 2006
"... The correct version of it is: Lemma 2.5 (Lai [1, Theorem 1]). If κ(G)�2, δ(G)�3, andif every edge of G lies in a 4cycle, then G is collapsible. Then Corollary 2.6 of [2] follows from this version of Lemma 2.5. The other error was the statement of Conjecture 2.7. The intended statement of Conjecture ..."
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of Conjecture 2.7 is: Conjecture 2.7. Every 2connected biclawfree graph G with δ(G)�4 has a spanning eulerian subgraph H with maximum degree Δ(H)�4. If G is a 2connected bipartite biclawfree graph with δ(G)�4, then by [2, Lemma 2.2], every edge of G lies in a 4cycle, and then by Lemma 2.5 (the correct
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Vl2: A scalable and flexible data center network
 In SIGCOMM
, 2009
"... To be agile and cost effective, data centers must allow dynamic resource allocation across large server pools. In particular, the data center network should provide a simple flat abstraction: it should be able to take any set of servers anywhere in the data center and give them the illusion that the ..."
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Cited by 443 (12 self)
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To be agile and cost effective, data centers must allow dynamic resource allocation across large server pools. In particular, the data center network should provide a simple flat abstraction: it should be able to take any set of servers anywhere in the data center and give them the illusion that they are plugged into a physically separate, noninterfering Ethernet switch with as many ports as the service needs. To meet this goal, we present VL2, a practical network architecture that scales to support huge data centers with uniform high capacity between servers, performance isolation between services, and Ethernet layer2 semantics. VL2 uses (1) flat addressing to allow service instances to be placed anywhere in the network, (2) Valiant Load Balancing to spread traffic uniformly across network paths, and (3) end system–based address resolution to scale to large server pools without introducing complexity to the network control plane. VL2’s design is driven by detailed measurements of traffic and fault data from a large operational cloud service provider. VL2’s implementation leverages proven network technologies, already available at low cost in highspeed hardware implementations, to build a scalable and reliable network architecture. As a result, VL2 networks can be deployed today, and we have built a working prototype. We evaluate the merits of the VL2 design using measurement, analysis, and experiments. Our VL2 prototype shuffles 2.7 TB of data among 75 servers in 395 s—sustaining a rate that is 94 % of the maximum possible. 1.
Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 369 (11 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
HAMILTON CYCLES AND QUOTIENTS OF BIPARTITE GRAPHS
, 1985
"... Paul Erdős conjectured that every graph in a certain family of bipartite graphs Gk.where k runs over the positive integers is Hamiltonian. We consider a quotient pseudograph ~ of G k such that a Hamilton path in ~ whose ends have one and two loops can be lifted to a Hamilton cycle in H. Edges k in ~ ..."
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Paul Erdős conjectured that every graph in a certain family of bipartite graphs Gk.where k runs over the positive integers is Hamiltonian. We consider a quotient pseudograph ~ of G k such that a Hamilton path in ~ whose ends have one and two loops can be lifted to a Hamilton cycle in H. Edges k
Planar Graphs, Regular Graphs, Bipartite Graphs and Hamiltonicity
, 1999
"... This paper seeks to review some ideas and results relating to Hamiltonian graphs. We list the well known results which are to be found in most undergraduate graph theory courses and then consider some old theorems which are fundamental to planar graphs. By restricting our attention to 3connected cu ..."
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Cited by 1 (0 self)
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interesting class of graphs are the bipartite graphs. In general these are not Hamiltonian but there is a famous conjecture due to Barnette that suggests that 3connected cubic bipartite planar graphs are Hamiltonian. In our final two sections we consider this along with another open conjecture due
HAMILTON DECOMPOSITIONS OF LINE GRAPHS OF SOME BIPARTITE GRAPHS
"... Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G). ..."
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Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).
Hamilton paths in grid graphs
 SIAM J. COMPUT
, 1982
"... A grid graph is a nodeinduced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes ..."
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Cited by 97 (0 self)
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A grid graph is a nodeinduced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two
TWO HAMILTON CYCLES IN BIPARTITE REFLECTIVE KNESER GRAPHS
, 1988
"... Let i and 7 be distinct positive integers. Let RG,,, be the bipartite graph whose vertices are the i and jsubsets of {0, 1,...,i+ j1} and whose adjacency is given by inclusion. We consider an Erdtis Conjecture that asserts that the graphs RG,,, are hamiltonian. In this paper Hamilton cycles in RG ..."
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Cited by 6 (2 self)
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Let i and 7 be distinct positive integers. Let RG,,, be the bipartite graph whose vertices are the i and jsubsets of {0, 1,...,i+ j1} and whose adjacency is given by inclusion. We consider an Erdtis Conjecture that asserts that the graphs RG,,, are hamiltonian. In this paper Hamilton cycles
Results 1  10
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