A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction
[chapter]
2014
Lecture Notes in Computer Science
Preserved Fulltext
We study the complexity of deciding whether a given signed graph admits a homomorphism to a fixed target signed graph [H, Σ], i.e. the (H, Σ)-Coloring problem. ...
Extending the notion of usual graph homomorphisms, homomorphisms of signed graphs were introduced, and have lead to some extensions and strengthenings in the theory of graph colorings and homomorphisms ...
Only recently, the development of the theory of homomorphisms of signed graphs has begun, see [10, 14] . This paper is the first study of the complexity of signed graph homomorphisms. ...
doi:10.1007/978-3-642-54423-1_46
fatcat:cudazm72vre5pjgoq3c24revui
Analogues of Cliques for (m, n)-Colored Mixed Graphs
2017
Graphs and Combinatorics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
complexity of a decision problem related to (0, 2)-cliques. ...
A homomorphism of an (m, n)-colored mixed graph G to an (m, n)-colored mixed graph H is a vertex mapping such that if uv is an arc (edge) of color c in G, then f (u)f (v) is also an arc (edge) of color ...
Question 1 . 1 . 11 Given an undirected simple graph, what is the complexity of deciding if it is the underlying graph of a signed clique? ...
doi:10.1007/s00373-017-1807-2
fatcat:b5s2qdfokfdj5g35ssakedgt3u
Oriented, 2-edge-colored, and 2-vertex-colored homomorphisms
2017
Information Processing Letters
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Finally, we prove that deciding if the 2-edge-colored chromatic number of a 2-edge-colored graph is at most 4 is NP-complete, even if restricted to 2-connected subcubic bipartite planar graphs with arbitrarily ...
Both reductions are rather long and follow the reduction to the case of oriented homomorphism in "Graphs and homomorphisms" by Hell and Nešetřil. ...
If a 2-edge-colored core H contains a monochromatic odd cycle of sign s, then the homomorphism to H restricted to input graphs containing only edges of sign s is NP-complete [6] . ...
doi:10.1016/j.ipl.2017.02.009
fatcat:q3qusqx7jjayfb4urvcjjy7c44
Analogous to cliques for (m,n)-colored mixed graphs
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this article, we mainly study different aspects of "cliques" for signed (graphs with positive or negative signs assigned to each edge) and switchable signed graphs (equivalence class of signed graph ...
Vertex coloring of a graph G with n-colors can be equivalently thought to be a graph homomorphism (edge preserving vertex mapping) of G to the complete graph K_n of order n. ...
We will avoid the definitions related to homomorphisms of signed graphs as it will make this article unnesessarily complicated. ...
arXiv:1411.7376v2
fatcat:lvryhvxwebfovk6k7de2x6kfyy
Homomorphism bounds of signed bipartite K4-minor-free graphs and edge-colorings of 2k-regular K4-minor-free multigraphs
2019
Discrete Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This supports a conjecture of Guenin claiming that every signed bipartite planar graph of unbalanced-girth 2k admits a homomorphism to SPC(2k) (this would be an extension of the four-color theorem). ...
A homomorphism of (G,Σ) to (H,Π) is a homomorphism of G to H which preserves the balance of closed walks. ...
Acknowledgments We thank the referees for carefully reading the original submission and helping to improve the presentation. ...
doi:10.1016/j.dam.2018.09.004
fatcat:zlnut5qj5faptddhasap5ae4pu
The complexity of signed graph and edge-coloured graph homomorphisms
2017
Discrete Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2015 pre-print arXiv:1510.05502v1 fatcat:dgp3np7g5jfixipbtye32yjs3uOther Versions
We study two types of homomorphisms of a signed graph (G,Σ) to a signed graph (H,Π): ec-homomorphisms and s-homomorphisms. ...
We study homomorphism problems of signed graphs from a computational point of view. ...
Another line of research is to study (H, Π)-Colouring for special instance restrictions, such as signed graphs whose underlying graph is planar or has bounded degree. ...
doi:10.1016/j.disc.2016.08.005
fatcat:vjiixa4e7vh3podx4w2oaxmzdy
Counting Problems in Parameterized Complexity
2019
International Symposium on Parameterized and Exact Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
graphs, and counting perfect matchings and Hamiltonian cycles in well-structured graphs. ...
After an introduction to the peculiarities of counting complexity, we survey the parameterized approach to counting problems, with a focus on two topics of recent interest: Counting small patterns in large ...
] to classify the complexity of counting homomorphism variants such as locally injective homomorphisms. ...
doi:10.4230/lipics.ipec.2018.1
dblp:conf/iwpec/Curticapean18
fatcat:tdfs7zngzrgv5fixf2qawrccuy
Circular Chromatic Number of Signed Graphs
2021
Electronic Journal of Combinatorics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Various notions of coloring of signed graphs have been studied. In this paper, we extend circular coloring of graphs to signed graphs. ...
A signed graph is a pair $(G, \sigma)$, where $G$ is a graph (loops and multi edges allowed) and $\sigma: E(G) \to \{+, -\}$ is a signature which assigns to each edge of $G$ a sign. ...
The complexity of signed graph and edge-coloured graph homomorphisms. Discrete Math., 340(2) (2017), 315-331.
References ...
doi:10.37236/9938
fatcat:5z46dr6kvncsxpsa6y4muo62qe
Concepts of signed graph coloring
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This paper surveys recent development of concepts related to coloring of signed graphs. Various approaches are presented and discussed. ...
One of them pointed out that there is a short survey on some aspects of coloring signed graphs by Lynn Takeshita [45] . ...
In general, the problem "Does a signed graph [G, σ ′ ] admit a homomorphism to [H, σ]?" is not easy to solve and its complexity has been studied e.g. in [4, 5, 14] . ...
arXiv:1909.09381v2
fatcat:uveiuweurrblxavntkdulqhb2m
On the Links of Vertices in Simplicial d-Complexes Embeddable in the Euclidean 2d-Space
2017
Discrete & Computational Geometry
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in p2d´1q-dimensional euclidean space. ...
Moreover, the bound is also true for the size of d-complexes linklessly embeddable in p2d'1q-dimensional space. ...
Acknowledgements The author is indebted to Herbert Edelsbrunner for bringing the Lemma 2 to his notice. ...
doi:10.1007/s00454-017-9936-1
fatcat:attp55r3kvah7efr2tjdmoihlm
Counting Subgraphs via Homomorphisms
[chapter]
2009
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. ...
polynomial, the classical algorithm of Kohn, Gottlieb, Kohn, and Karp for counting Hamiltonian cycles, Ryser's formula for counting perfect matchings of a bipartite graph, and color coding based algorithms ...
Acknowledgement Many thanks to László Lovász for answering our questions on graph homomorphisms. ...
doi:10.1007/978-3-642-02927-1_8
fatcat:uw247ph62rbnjeggb2k3ysqq3y
Counting Subgraphs via Homomorphisms
2012
SIAM Journal on Discrete Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. ...
polynomial, the classical algorithm of Kohn, Gottlieb, Kohn, and Karp for counting Hamiltonian cycles, Ryser's formula for counting perfect matchings of a bipartite graph, and color coding based algorithms ...
Acknowledgement Many thanks to László Lovász for answering our questions on graph homomorphisms. ...
doi:10.1137/100789403
fatcat:igr4ivf2z5gg3h3zabvnwnfifm
On a graph property generalizing planarity and flatness
2009
Combinatorica
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
This parameter characterizes subgraphs of paths, outerplanar graphs, planar graphs, and graphs that have a flat embedding as those graphs G with σ(G) ≤ 1, 2, 3, and 4, respectively. ...
Among several other theorems, we show that if H is a minor of G, then σ(H) ≤ σ(G), that σ(Kn) = n−1, and that if H is the suspension of G, then σ(H) = σ(G)+1. ...
One step in proving this, is to show that planar graphs G have σ(G) ≤ 3. A planar graph G clearly has an even mapping in R 2 . Hence I(z) = 0 for each symmetric 2-cycle z of D(G). ...
doi:10.1007/s00493-009-2219-6
fatcat:7uzysghijzbbzm2t4qz4ygjo2m
On links of vertices in simplicial d-complexes embeddable in the euclidean 2d-space
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
These considerations lead us to a new upper bound on the total number of d-simplices in an embeddable complex in 2d-space with n vertices, improving known upper bounds, for all d ≥ 2. ...
In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (2d-1)-dimensional euclidean space. ...
Acknowledgements The author is indebted to Herbert Edelsbrunner for bringing Lemma 2 to his notice. ...
arXiv:1512.05164v8
fatcat:p5oh4vnaffad7grd77zx756r5y
Quasi-isometrically embedded subgroups of braid and diffeomorphism groups
2007
Transactions of the American Mathematical Society
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D ...
2 , ∂D 2 , vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L 2 -norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings ...
We also thank Benson Farb for pointing out to us the work of Januszkiewicz andŚwiatkowski [7] and its relevance to the present work, and in particular the existence of hyperbolic 4-manifold subgroups ...
doi:10.1090/s0002-9947-07-04332-2
fatcat:wfytxzvc2rfldmtp26d6ub6vui
« Previous
Showing results 1 — 15 out of 1,362 results