Now showing items 1-20 of 38

• #### A rainbow Dirac's theorem ﻿

(2020-01-01)
Article
Open Access
A famous theorem of Dirac states that any graph on n vertices with minimum degree at least n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton ...
• #### Acyclic edge colourings of graphs with large girth ﻿

(2016-11-03)
Article
Open Access
An edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least ...
• #### AM2: Examen MQ: primavera 2019 ﻿

(Universitat Politècnica de Catalunya, 2019-04-03)
Exam
• #### An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs ﻿

(2014)
Conference report
Open Access
We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by ...
• #### Búsqueda de comunidades en grafos grandes mediante configuraciones implícitas de vectores ﻿

Conference report
Open Access
Presentamos el algoritmo OCA para buscar comunidades solapadas en grafos grandes, como por ejemplo la Wikipedia con 1,6×107 nodos y 1,8×108 aristas. OCA se basa en la búsqueda iterativa de subconjuntos localmente óptimos ...
• #### Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture ﻿

(2018-09-17)
Article
Open Access
A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, ...
• #### Continuous symmetry and shape measures ﻿

(Centre de Recerca Matemàtica, 2010-06)
Part of book or chapter of book
Open Access
• #### Correlation among runners and some results on the lonely runner conjecture ﻿

(2016-10-03)
Article
Open Access
The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where ...
• #### Counting independent sets in cubic graphs of given girth ﻿

(2018-09-26)
Article
Open Access
We prove a tight upper bound on the independence polynomial (and total number of independent sets) of cubic graphs of girth at least 5. The bound is achieved by unions of the Heawood graph, the point/line incidence graph ...
• #### Critical percolation on random regular graphs ﻿

(2018-03-20)
Article
Open Access
We show that for all $d\in \{3,\ldots ,n-1\}$ the size of the largest component of a random $d$-regular graph on $n$ vertices around the percolation threshold $p=1/(d-1)$ is $\Theta (n^{2/3})$, with high probability. ...
• #### Decomposition of bounded degree graphs into C4-free subgraphs ﻿

(2014-10-15)
Article
Open Access
We prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated ...
• #### Desenvolupament d'una càmera digital per a la visió estéreo en temps real. ﻿

(2008-12-04)
Audiovisual
Open Access
• #### Diameter and stationary distribution of random r-out digraphs ﻿

(2020-08-07)
Article
Open Access
Let D(n, r) be a random r-out regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r = 2, there exists ¿r > 0 such that diam(D(n, r)) = (1 + ¿r + o(1)) logr n. The ...
• #### Existence of spanning F-free subgraphs with large minimum degree ﻿

(2016-12-07)
Article
Restricted access - publisher's policy
Let F be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning F-free subgraph of G with large minimum degree. This problem is well understood if F does not contain ...
• #### Fast recoloring of sparse graphs ﻿

(2015-09-07)
Article
Open Access
In this paper, we show that for every graph of maximum average degree bounded away from d and any two (d + 1)-colorings of it, one can transform one coloring into the other one within a polynomial number of vertex recolorings ...
• #### Frozen (¿ + 1)-colourings of bounded degree graphs ﻿

(2020-10-19)
Article
Restricted access - publisher's policy
Let G be a graph on n vertices and with maximum degree ¿, and let k be an integer. The k-recolouring graph of G is the graph whose vertices are k-colourings of G and where two k-colourings are adjacent if they differ at ...
• #### How to determine if a random graph with a fixed degree sequence has a giant component ﻿

(Institute of Electrical and Electronics Engineers (IEEE), 2016)
Conference report
Open Access
The traditional Erdos-Renyi model of a random network is of little use in modelling the type of complex networks which modern researchers study. In this graph, every pair of vertices is equally likely to be connected by ...
• #### How to determine if a random graph with a fixed degree sequence has a giant component ﻿

(2017-01-26)
Article
Open Access
For a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, ...
• #### Improved bounds for randomly sampling colorings via linear programming ﻿

(2019)
Conference report
Restricted access - publisher's policy
A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of k-colorings of a graph G on n vertices with maximum degree ¿ is rapidly mixing for k = ¿ + 2. In FOCS 1999, Vigoda ...
• #### Large subgraphs without short cycles ﻿

(2015-01-06)
Article
Open Access
We study two extremal problems about subgraphs excluding a family F of graphs. i) Among all graphs with m edges, what is the smallest size f(m, F) of a largest F–free subgraph? ii) Among all graphs with minimum degree d ...