Results 41 to 50 of about 1,862,441 (301)
Coalition structure generation over graphs [PDF]
, 2012 We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into ...
Polukarov, Maria +5 more
core +1 more source
Vertex sparsifiers : new results from old techniques [PDF]
, 2014 Given a capacitated graph $G = (V,E)$ and a set of terminals $K \subseteq V$, how should we produce a graph $H$ only on the terminals $K$ so that every (multicommodity) flow between the terminals in $G$ could be supported in $H$ with low congestion, and ...
Gupta, Anupam +10 more
core +1 more source
on the number of cliques and cycles in graphs [PDF]
Transactions on Combinatorics, 2013 We give a new recursive method to compute the number of cliques and cycles of a graph. This method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the ...
Mojgan Emami, Masoud Ariannejad
doaj
Testing first-order properties for subclasses of sparse graphs [PDF]
, 2013 We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez.
Thomas, Robin +2 more
core +1 more source
On the choosability of -minor-free graphs
Combinatorics, Probability and Computing, 2023 AbstractGiven a graph $H$ , let us denote by $f_\chi (H)$ and $f_\ell (H)$ , respectively, the maximum chromatic number and the maximum list chromatic number of $H$ -minor-free graphs. Hadwiger’s famous colouring conjecture from 1943 states that $f_\chi (K_t)=t-1$ for every $t \ge 2$ .
Olivier Fischer, Raphael Steiner
openaire +3 more sources
The inverse eigenvalue problem of a graph: Multiplicities and minors [PDF]
J. Comb. Theory B, 2017 The inverse eigenvalue problem of a given graph $G$ is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G$. Barrett et al.
W. Barrett +8 more
semanticscholar +1 more source
Graph minors and the crossing number of graphs
Electronic Notes in Discrete Mathematics, 2007 Abstract There are three general lower bound techniques for the crossing numbers of graphs, all of which can be traced back to Leighton's work on applications of crossing number in VLSI: the Crossing Lemma, the Bisection Method, and the Embedding Method. In this contribution, we sketch their adaptations to the minor crossing number.
Drago Bokal +3 more
openaire +1 more source
On matroids of branch-width three [PDF]
, 2001 For the abstract of this paper, please see the PDF ...
Whittle, G +15 more
core +1 more source
Unavoidable parallel minors of regular matroids
, 2011 This is the post-print version of the Article - Copyright @ 2011 ElsevierWe prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M (K_{3,k}), M(W_k), M(K_k), the cycle matroid of
Chun, Carolyn +5 more
core +1 more source
Coloring graphs with forbidden minors
Journal of Combinatorial Theory, Series B, 2017 Hadwiger's conjecture from 1943 states that for every integer $t\ge1$, every graph either can be $t$-colored or has a subgraph that can be contracted to the complete graph on $t+1$ vertices. As pointed out by Paul Seymour in his recent survey on Hadwiger's conjecture, proving that graphs with no $K_7$ minor are $6$-colorable is the first case of ...
Martin Rolek, Zi-Xia Song
openaire +4 more sources