[PDF] Top 20 The complexity of signed and edge-coloured graph homomorphisms.
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The complexity of signed and edge-coloured graph homomorphisms.
... problems of signed graphs from a computational point of ...A signed graph (G, Σ) is a graph G where each edge is given a sign, positive or negative; Σ ⊆ E(G) denotes ... Voir le document complet
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On the Parameterized Complexity of Graph Modification to First-Order Logic Properties
... is the graph modification problem asking whether one can remove at most k vertices such that the resulting graph has no edges (we use u ∼ v for the adjacency ...a graph class ... Voir le document complet
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The Rank-Width of Edge-Coloured Graphs
... results of rank-width, the fact that clique-width is defined for graphs - directed or not, with edge colors or not - is an un- deniable advantage over ...notion of rank-width for ... Voir le document complet
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The homomorphism order of signed graphs
... a signed graph (G, σ) could be simply viewed as a 2-edge-colored graph, usually associating positive edges with color blue (or with solid lines) and negative edges with color red (or ... Voir le document complet
15
The Bipartite Swapping Trick on Graph Homomorphisms
... d-regular graph G, and positive integer n, iðG; nÞ ≤ iðK d;d ; nÞ N ∕ ð2dÞ : The collection I ðG; nÞ arises naturally in statistical mechanics [9] and communica- tion networks [4], ...to ... Voir le document complet
22
Bounding signed series-parallel graphs and cores of signed K 4 -subdivisions
... any signed graph in G ij , every cycle of it is either of type 00 or of type ...cycle of length l will be denoted by C l + (C l − ). 2.2 Homomorphisms and bounds A ... Voir le document complet
32
On the 2-edge-coloured chromatic number of grids
... kinds of modified graphs, called oriented graphs and 2-edge-coloured ...oriented graph − → G is a directed graph obtained from an undirected simple graph G by orienting ... Voir le document complet
15
Oriented, 2-edge-colored, and 2-vertex-colored homomorphisms
... By the previous arguments, J e maps to T e if and only if J v maps to T v ...4 Complexity of 2-edge-colored homomorphism In this section, we investigate the case of ... Voir le document complet
10
Complexity of greedy edge-colouring
... colouring of many graph classes has also been studied. One of the classes is the one of line ...graphs. The line graph of a graph G, denoted L(G), is ... Voir le document complet
9
Complexity of greedy edge-colouring
... colouring of many graph classes has also been studied. One of the classes is the one of line ...graphs. The line graph of a graph G, denoted L(G), is ... Voir le document complet
14
Complexity of determining the irregular chromatic index of a graph
... For the same reasons as before, the edges b i,1 w 1 , ...be coloured 1 (resp. 0) in any extension of φ to G F (` i ...Therefore, the vertex w 1 is adjacent to vertices with degree n i + ... Voir le document complet
17
Classification of edge-critical underlying absolute planar cliques for signed graphs
... lower and upper bounds on different parameters for the family of outerplanar ...rel and ω abs denote the chromatic number, relative clique number and absolute clique number for ... Voir le document complet
17
Homomorphisms of partial t-trees and edge-coloring of partial 3-trees
... that the restriction of Seymour’s conjecture on cubic (planar) graphs is Tait’s reformulation of the four-color ...for the larger class of K 5 -minor-free graphs (which includes ... Voir le document complet
21
Complexity of planar signed graph homomorphisms to cycles
... graphs and switching homomorphisms. Signed graphs are special types of 2-edge-coloured graphs, whose edge-colours represent signs: positive and ...a signed ... Voir le document complet
18
Homomorphisms of sparse signed graphs
... by the examples in Section 9. For the special case of k = 3, Conjecture 14 claims that every planar signed bipar- tite graph with unbalanced-girth at least 10 admits a homomorphism to U ... Voir le document complet
27
The complexity of tropical graph homomorphisms.
... is of order 3, then all its vertices belong to each 6-cycle of ...2.12 and (H, c)-Colouring is polynomial-time ...subgraph the path on three vertices where the central vertex is Blue ... Voir le document complet
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Homomorphisms of signed graphs: An update
... choice of C W ’s. Thus a first necessary condition for W to be the set of negative closed walks in (G, σ) for some choice of σ is that the two sets {C W | W ∈ W} and {C W | W / ∈ ... Voir le document complet
28
Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture
... convinced of this statement, just consider the following con- ...from the 2-edge-connected graph G depicted in Figure 1, which admits no P 9 ...2-edge-connected graph with ... Voir le document complet
25
On the Complexity of Distributed Graph Coloring with Local Minimality Constraints
... Unité de recherche INRIA Futurs Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy[r] ... Voir le document complet
18
Homomorphism bounds of signed bipartite K4-minor-free graphs and edge-colorings of 2k-regular K4-minor-free multigraphs
... graph of unbalanced-girth at least 2k, our algorithm builds a homomorphism of (G, Σ) to (B, ...general signed graph (B, Π), it can be checked in polynomial time whether it is a ... Voir le document complet
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