hamiltonian cycles in random graphs

... Hashing 5.5.1 Chain Hashing 5.5.2 Hashing: Bit Strings 5.5.3 Bloom Filters 5.5.4 Breaking Symmetry Random Graphs 5.6.1 Random Graph Models 5.6.2 Application: Hamiltonian Cycles in Random Graphs ... ( V, E ) with n vertices the minimum cut - or min-cut - problem is to fi nd a minimum cardinality cut-set in G Minimum cut problems arise in many contexts, including the study of network reliability ... player to have a winning tic-tac-toe combination wins the game, and a tie occurs if nei­ ther player achieves a winning combination Find the probability that each player wins (Agai n , you may...

Ngày tải lên: 14/07/2016, 15:42

... Nguyen Probability for Computing 19 Balls into Bins We have m balls that are thrown into n bins, with the location of each ball chosen independently and uniformly at random from n possibilities ... transmitted after the last sampled packet until and including the next sampled packet is geometrically distributed From the point of destination host, determining all the routers on the path is like a ... distribution of the balls into the bins look like    “Birthday paradox” question: is there a bin with at least balls How many of the bins are empty? How many balls are in the fullest bin? Answers to...

Ngày tải lên: 12/07/2014, 18:20

... balls in a bin: (lnn/lnlnn) if choose m=n Another disadvantage: wasting a lot of space in empty bins © 2010, Van Nguyen Probability for Computing 10 Hashing: bit strings In chain hashing, n ... placing items from the universe U into n bins Here, U consists of all possible password strings The collection of bins called hash table Chain hashing: items that fall into the same bin are chained ... each pwd into a 32-bit string, i.e a fingerprint We store the dictionary of fingerprints of the unacceptable passwords When checking a password, compute its fingerprint then check it against the...

Ngày tải lên: 12/07/2014, 18:20

... coloring Covering graphs, double coverings Duality (graphs, matroids, or matrices) Enumeration of types of signed graphs, etc Even-cycle matroids Edge coloring Expository Interesting exercises (in ... frustration index (line index of imbalance) Connections with geometry, including toric varieties, complex complement, etc Digraphs with gains (or voltages) Generalization Gain graphs, voltage graphs, ... detecting cycles in periodic graphs J Assoc Comput Mach 40 (1993), 791–830 MR 96h:05182 Zbl 782.68053 Looking for a closed walk (“cycle”) with gain in a gain digraph with (additive) gains in Qd...

Ngày tải lên: 07/08/2014, 05:23

... matrix with elements in a ring The following definition is a generalization of the matrix rank over fields to matrices over rings: Definition Let R be a ring and let n be a positive integer We say, that ... given as a linear combination of some Qkj ’s, each kj > i.) Consequently, n≤ r+p−2 + ≤ (r + p)p−1 p−1 (3) We are interested in the following question: Question Let R = Zm , what is the minimum rank ... n(log log n) Constructing Low Rank mod Co-Diagonal Matrices In this section we prove Theorems and Our main tool is the following theorem (choosing m = and = 2): Theorem 10 (Barrington, Beigel, Rudich[3])...

Ngày tải lên: 07/08/2014, 06:20

... terminate in at most n/χ steps and in the end there will be no short quasicycles We show now that we have created neither long cycles nor long quasicycles Indeed, by (b), during the edge reversing ... directed quasicycle (Since G is triangle-free, we can always this.) Since G satisfies (a), i.e., in particular it contains vertex disjoint short cycles the electronic journal of combinatorics (2000), ... Bollob´s, Colouring lattices, Alg Universalis (1977), 313–314 a [3] B Bollob´s, Random Graphs, Academic Press 1985 a [4] B Bollob´s, G Brightwell and J Neˇetˇil, Random Graphs and Covering Graphs a...

Ngày tải lên: 07/08/2014, 06:20

... question of finding a combinatorial interpretation of the above identity (1.2) In this paper, we obtain a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation ... present a parity reversing involution on connected noncrossing graphs and obtain an expression for the number dn,k in terms of the numbers Nn,m An involution on noncrossing trees In this section, ... noncrossing tree Hough [5] found a combinatorial interpretation of the relation between the descent generating function of noncrossing trees and the generating function for connected noncrossing graphs...

Ngày tải lên: 07/08/2014, 13:21

... and so has an even number of hamiltonian cycles Suppose v is the twin of some v ∈ V (G) If v ∈ V (H), then H has an even number of hamiltonian cycles since H is an induced subgraph of G If v ∈ ... complete, then G either contains an induced cycle Ck with k ≥ or an induced K1,1,2 In either case, G contains an induced subgraph of order four or more that is uniquely hamiltonian The second part ... induced subgraph of order three or more is uniquely hamiltonian, which is also equivalent to every induced subgraph of order three or more having an even number (zero) of hamiltonian cycles In...

Ngày tải lên: 07/08/2014, 15:22

... mutually nonadjacent and distinct Hence, s r − The lemma is proved Terwilliger graphs In this section we give a definition of Terwilliger graphs and some useful facts concerning them A Terwilliger graph ... − 48 = are not integers, a contradiction In the remaining case, when ∆ is regular with degree 57, we get the same contradiction The lemma is proved The next lemma will be used in the proof of ... exists a c-coclique in Γ1 (x) containing y, z Then µ−1 max{ c′ (λ + 1) − k c′ c′ |2 c}, and, if equality is attained, then Γ is a Terwilliger graph Proof Let Γ1 (x) contain a coclique C ′ on...

Ngày tải lên: 08/08/2014, 12:22

... Unicyclic graphs Ui (1 i 7) Moreover, Shao et al [12] determined the last six graphs (according to their smallest algebraic connectivities) among all connected graphs in Gn when n In this six graphs, ... the proof Connected graphs In Section 3, we determined the last four bicyclic graphs according to their smallest algebraic connectivities among all graphs in Bn with n 13 Combing with the results ... unicyclic graphs (according to their smallest algebraic connectivities) are determined as U1 , U2 and U3 (shown in Fig 2), respectively In [9], we further determine the fourth to seventh unicyclic graphs, ...

Ngày tải lên: 08/08/2014, 12:23

... row has all but one in the same column as the other row In this paper, we continue the study of thin Lehman matrices We investigate the Johnson subgraphs associated to thin Lehman matrices, which ... ∈ [j + 1, r) We have thus determined the columns [k + r − 1] in A This determines A up to a choice of σ([r, n − k]) Since all 1s in rows [k] of A are contained in columns [k + r − 1], we can permute ... uniquely determines the corresponding rows in the Lehman matrix, and we completely classified matrices where their graphs have two connected components Lehman matrices with graphs containing more connected...

Ngày tải lên: 08/08/2014, 12:23

... decades later The number of men in this sector remained stable over the period, at around 700 000 Women also made gains in both the finance/banking industries and in the defence-related public ... women worked in finance and banking institutions in 1975, the number increased to 450 000 by 1995 The number of men grew only marginally from 425 000 to 480 000 over the same period In defence, ... brought significant changes in the representation of women in Freedonia's work force, according to the graphs In 1975, for example, some 300 000 men and 250 000 women worked in the communications sector...

Ngày tải lên: 04/10/2012, 10:02

... 1.1Using Graphs and Tables TASK 'Which of the following statements you think best describe the purpose of providing graphs and tables in an academic text? a) to explain what is in the t€xt in a ... common ones: for in -and between during before from-to/until after 13 14 Writing Tables and Diagrams Visuals: about Graphs, in: In 1999 In the 20th century In the first ten years in tltere was ... development expansion j,r-p gain decrease growth doubling rise diminishing lowering drop downturn decline fall depletion lessening fluctuation Tables Visuals: Writing about Graphs, and Diagrams TASK...

Ngày tải lên: 04/10/2012, 10:02

... 1.1Using Graphs and Tables TASK 'Which of the following statements you think best describe the purpose of providing graphs and tables in an academic text? a) to explain what is in the t€xt in a ... common ones: for in -and between during before from-to/until after 13 14 Writing Tables and Diagrams Visuals: about Graphs, in: In 1999 In the 20th century In the first ten years in tltere was ... development expansion j,r-p gain decrease growth doubling rise diminishing lowering drop downturn decline fall depletion lessening fluctuation Tables Visuals: Writing about Graphs, and Diagrams TASK...

Ngày tải lên: 04/09/2013, 15:20

... invalid paths by inserting two nodes at the same time For instance, try disabling the row count check and inserting a subordinate first, followed by a manager, in the same statement: INSERT INTO ... 28, 46 statement blocks, 45–46 testing, 36–39 validating input, 40–42 binary encoding, 395 binary floating-point coordinate values, 298 Binary hash values, 148 Bing Maps, 308 420 bitemporal data ... Streets VALUES (6, 'Lexington'); GO New intersections INSERT INTO Intersections VALUES (5, 'E'), (6, 'F'), (7, 'G'), (8, 'H'); GO New intersection/street mappings INSERT INTO IntersectionStreets...

Ngày tải lên: 05/10/2013, 08:48

... common ones: for in -and between during before from-to/until after 13 14 Writing Tables and Diagrams Visuals: about Graphs, in: In 1999 In the 20th century In the first ten years in tltere was ... declinedsignificantQ at: At the end of the last century tltere utasa sharp increase manufacturing in since: Since the 19th century there has beena steadyd.ecline are: Orher usefulexpressions (in) ... found in buildings Both in outsideeating areasand in skips compostable materials, uhich total Consideringthe 40o/o the of of waste collectedin the uniuersity, it is could be recycled re-usedin someuay...

Ngày tải lên: 25/10/2013, 07:20

... back into the air Tbe action of lightning and offee-liuing nitrogen-f.xing bacteria carriesthe nitrogen into the soil At tlte sametime somenitrogen-fixing bacteria in the nodulesof leguminousplants ... incorrectsentence, information 2,3, and arc correctbut is not very good in sryle It Expenditure cannot hauean increase can, however, increaseasinsentence is correct 7.Here the verb happenis inappropriate ... uterein arranged marriages,and only around 22o/o had loue marriages,by 1990 this proportion taasinuerted, uith B3o/obeing in loue marriagesand on$ 15%oinuolued in arranged marriages are: 26 The incorrect...

Ngày tải lên: 25/10/2013, 07:20

... Exam Areas Graphs Information may be displayed in many ways The three basic types of graphs you should know are bar graphs, line graphs, and pie graphs (or pie charts) Bar Graphs Bar graphs convert ... Drink 10% Medical 7% nt e inm r ta te En s 5% Saving Other 12% Medical 7%nt e inm r ta te En s 4% Saving Other 25% Housing 1970 Average Income $12,000 188 22% Food and Drink Team-LRN 32% Housing ... of income spent on housing in 1970 to income spent on housing in 1975? A to B to C 25 to 32 D to E to What was the percent increase from 1970 to 1975 in the percentage spent on food and drink?...

Ngày tải lên: 01/11/2013, 14:20

... (2008) 103-109 The general model conflicting chip firing games In this section after giving the definition of the model Conflicting Chip Firing Games (CCFG), we investigate the relation between its ... “Conflicting Chip Firing Game” (CCFG) Further, we constate that, in this new model, by relaxing the condition about the number of chips in a vertex, the evolution rule is much more flexible In other ... this set, we define the following relation: a ≥ b if b can be obtained from a by applying a sequence of firings In order to describe the evolution of a CCFG on graph G, we introduce the evolution matrix...

Ngày tải lên: 12/02/2014, 17:20