Author image not provided
 Bruce A Reed

Authors:
Add personal information
  Affiliation history
Bibliometrics: publication history
Average citations per article11.20
Citation Count1,422
Publication count127
Publication years1987-2016
Available for download18
Average downloads per article412.67
Downloads (cumulative)7,428
Downloads (12 Months)341
Downloads (6 Weeks)35
SEARCH
ROLE
Arrow RightAuthor only
· Advisor only
· All roles


AUTHOR'S COLLEAGUES
See all colleagues of this author

SUBJECT AREAS
See all subject areas




BOOKMARK & SHARE


127 results found Export Results: bibtexendnoteacmrefcsv

Result 1 – 20 of 127
Result page: 1 2 3 4 5 6 7

Sort by:

1
January 2016 Journal of Graph Theory: Volume 81 Issue 1, January 2016
Publisher: John Wiley & Sons, Inc.
Bibliometrics:
Citation Count: 0

In 1998 the second author proved that there is an ε>0 such that every graph satisfies ï��ï��ï��1-εΔ+1+εωï��. The first author recently proved that any graph satisfying ω>23Δ+1 contains a stable set intersecting every maximum clique. In this note, we exploit the latter result to give a much shorter, simpler proof ...
Keywords: chromatic number, maximum degree, clique number, Reed's Conjecture, graph coloring

2
June 2015 Journal of Graph Theory: Volume 79 Issue 2, June 2015
Publisher: John Wiley & Sons, Inc.
Bibliometrics:
Citation Count: 3

We prove a conjecture of Ohba that says that every graph G on at most 2�G+1 vertices satisfies ��G=�G.
Keywords: chromatic-choosable, graphs, choosability, list coloring

3
March 2015 Journal of Graph Theory: Volume 78 Issue 3, March 2015
Publisher: John Wiley & Sons, Inc.
Bibliometrics:
Citation Count: 2

The second author's B.A.R. ω, Δ, ï�� conjecture proposes that every graph satisfies ï��ï��ï��12Δ+1+ωï��. In this article, we prove that the conjecture holds for all claw-free graphs. Our approach uses the structure theorem of Chudnovsky and Seymour. Along the way, we discuss a stronger local conjecture, and prove that it ...
Keywords: Reed's conjecture, graph coloring, chromatic number, claw-free graph

4
November 2014 Journal of Combinatorial Theory Series B: Volume 109 Issue C, November 2014
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

We consider the chromatic number of graphs with maximum degree Δ. For sufficiently large Δ, we determine the precise values of k for which the barrier to ( Δ + 1 - k ) -colourability must be a local condition, i.e. a small subgraph. We also show that for Δ ...
Keywords: Brooks' Theorem, Chromatic number

5
October 2014 Random Structures & Algorithms: Volume 45 Issue 3, October 2014
Publisher: John Wiley & Sons, Inc.
Bibliometrics:
Citation Count: 0

Keywords: H-free graph, homogeneous set, Erdős-Hajnal

6
January 2013 SODA '13: Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 10
Downloads (6 Weeks): 1,   Downloads (12 Months): 8,   Downloads (Overall): 85

Full text available: PDFPDF
A key result of Robertson and Seymour's graph minor theory is a structure theorem stating that all graphs excluding some fixed graph as a minor have a tree decomposition into pieces that are almost embeddable in a fixed surface. Most algorithmic applications of graph minor theory rely on an algorithmic ...

7
November 2012 Combinatorics, Probability and Computing: Volume 21 Issue 6, November 2012
Publisher: Cambridge University Press
Bibliometrics:
Citation Count: 4

A class <private-char><inline-graphic mime-subtype="gif" xlink="S0963548312000272_char1" xlink:type="simple"/></private-char> of labelled graphs is bridge-addable if, for all graphs G in <private-char><inline-graphic mime-subtype="gif" xlink="S0963548312000272_char1" xlink:type="simple"/></private-char> and all vertices u and v in distinct connected components of G , the graph obtained by adding an edge between u and v is also in <private-char><inline-graphic mime-subtype="gif" ...
Keywords: Primary 05C80, Secondary 60C05

8
April 2012 European Journal of Combinatorics: Volume 33 Issue 3, April, 2012
Publisher: Academic Press Ltd.
Bibliometrics:
Citation Count: 10

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an @[email protected]? grid minor is exponential in @?. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor ...

9
April 2012 Discrete Applied Mathematics: Volume 160 Issue 6, April, 2012
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 12

Clique-width is a relatively new parameterization of graphs, philosophically similar to treewidth. Clique-width is more encompassing in the sense that a graph of bounded treewidth is also of bounded clique-width (but not the converse). For graphs of bounded clique-width, given the clique-width decomposition, every optimization, enumeration or evaluation problem that ...
Keywords: Clique-width computation, Polynomial-time algorithm

10
March 2012 Journal of Combinatorial Theory Series B: Volume 102 Issue 2, March, 2012
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 26

We consider the following well-known problem, which is called the disjoint paths problem. For a given graph G and a set of k pairs of terminals in G, the objective is to find k vertex-disjoint paths connecting given pairs of terminals or to conclude that such paths do not exist. ...
Keywords: Graph minor, Tree-width, Disjoint paths, Quadratic time

11
February 2012 SIAM Journal on Discrete Mathematics: Volume 26 Issue 1, January 2012
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 7

An $L(p,1)$-labeling of a graph is a function $f$ from the vertex set to the positive integers such that $|f(x)-f(y)|\geqslant p$ if dist$(x,y)=1$ and $|f(x)-f(y)|\geqslant 1$ if dist$(x,y)=2$, where dist$(x,y)$ is the distance between the two vertices $x$ and $y$ in the graph. The span of an $L(p,1)$-labeling $f$ is ...
Keywords: graph coloring, channel assignment, graph labeling, generalized coloring

12
October 2011 FOCS '11: Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 6

We generalize the seminal Graph Minor algorithm of Robertson and Seymour to the parity version. We give polynomial time algorithms for the following problems:\begin{enumerate}\itemthe parity $H$-minor (Odd $K_k$-minor) containment problem, and\itemthe disjoint paths problem with $k$ terminals and the parity condition for each path, \end{enumerate}as well as several other related ...
Keywords: Odd minor, parity minor, odd cycles and the parity disjoint paths problem

13
January 2011 SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 0

The term Probabilistic Method refers to the proof of deterministic statements using probabilistic tools. The method has been successfully applied to a number of problems in the field of graph colouring. We survey some of the results thereby obtained. The talk is intended to be accessible and short on details. ...

14
January 2011 Journal of Combinatorial Theory Series B: Volume 101 Issue 1, January, 2011
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 2

Let H be a graph. If G is an n-vertex simple graph that does not contain H as a minor, what is the maximum number of edges that G can have? This is at most linear in n, but the exact expression is known only for very few graphs H. ...
Keywords: Minors, Extremal, Graph

15
October 2010 FOCS '10: Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 9

It is shown that for each $t$, there is a separator of size $O(t \sqrt{n})$ in any $n$-vertex graph $G$ with no $K_t$-minor. This settles a conjecture of Alon, Seymour and Thomas (J. Amer. Math. Soc., 1990 and STOC'90), and generalizes a result of Djidjev (1981), and Gilbert, Hutchinson and ...
Keywords: separator, excluded minor, and divide and conquer

16 published by ACM
June 2010 STOC '10: Proceedings of the forty-second ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 10
Downloads (6 Weeks): 5,   Downloads (12 Months): 46,   Downloads (Overall): 434

Full text available: PDFPDF
We consider the following problem, which is called the odd cycle packing problem . Input: A graph $G$ with n vertices and m edges, and an integer k. Output: k vertex disjoint odd cycles. We also consider the edge disjoint case, and the node- and arc-disjoint directed case. This problem ...
Keywords: odd cycle, packing

17
April 2010 Discrete Applied Mathematics: Volume 158 Issue 7, April, 2010
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 6

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is ...
Keywords: i-triangulated graph, Clique-separable graph, Graph algorithm, Tree decomposition

18
March 2010 Journal of Combinatorial Theory Series B: Volume 100 Issue 2, March, 2010
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 4

We prove that every graph with maximum degree @D can be properly (@D+1)-coloured so that no colour appears more than O([email protected]/[email protected]) times in the neighbourhood of any vertex. This is best possible up to the constant multiple in the O(-) term.

19
March 2010 Journal of Combinatorial Theory Series B: Volume 100 Issue 2, March, 2010
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

We correct an error that appears in [M. Molloy, B. Reed, Asymptotically optimal frugal colouring, J. Combin. Theory Ser. B 100 (2) (2010) 226-246, this issue].

20
January 2010 SODA '10: Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 17
Downloads (6 Weeks): 0,   Downloads (12 Months): 8,   Downloads (Overall): 104

Full text available: PDFPDF
We consider the following problem, which is called the odd cycles transversal problem . Input: A graph G and an integer k . Output: A vertex set X ∈ V(G) with | X | ≤ k such that G -- X is bipartite. We present an O(mα(m, n )) time ...
Keywords: Erdős-Pósa property, nearly linear time algorithm, half-integral disjoint odd cycles packing



The ACM Digital Library is published by the Association for Computing Machinery. Copyright © 2018 ACM, Inc.
Terms of Usage   Privacy Policy   Code of Ethics   Contact Us