1,713 research outputs found
Forbidden Directed Minors and Kelly-width
Partial 1-trees are undirected graphs of treewidth at most one. Similarly,
partial 1-DAGs are directed graphs of KellyWidth at most two. It is well-known
that an undirected graph is a partial 1-tree if and only if it has no K_3
minor. In this paper, we generalize this characterization to partial 1-DAGs. We
show that partial 1-DAGs are characterized by three forbidden directed minors,
K_3, N_4 and M_5
On some special classes of contact -VPG graphs
A graph is a -VPG graph if one can associate a path on a rectangular
grid with each vertex such that two vertices are adjacent if and only if the
corresponding paths intersect at at least one grid-point. A graph is a
contact -VPG graph if it is a -VPG graph admitting a representation
with no two paths crossing and no two paths sharing an edge of the grid. In
this paper, we present a minimal forbidden induced subgraph characterisation of
contact -VPG graphs within four special graph classes: chordal graphs,
tree-cographs, -tidy graphs and -free graphs. Moreover, we present a
polynomial-time algorithm for recognising chordal contact -VPG graphs.Comment: 34 pages, 15 figure
Graph quasivarieties
Introduced by C. R. Shallon in 1979, graph algebras establish a useful
connection between graph theory and universal algebra. This makes it possible
to investigate graph varieties and graph quasivarieties, i.e., classes of
graphs described by identities or quasi-identities. In this paper, graph
quasivarieties are characterized as classes of graphs closed under directed
unions of isomorphic copies of finite strong pointed subproducts.Comment: 15 page
Minimum Cost Homomorphisms to Reflexive Digraphs
For digraphs and , a homomorphism of to is a mapping $f:\
V(G)\dom V(H)uv\in A(G)f(u)f(v)\in A(H)u \in V(G)c_i(u), i \in V(H)f\sum_{u\in V(G)}c_{f(u)}(u)H, the {\em minimum cost homomorphism problem} for HHGc_i(u)u\in V(G)i\in V(H)kGHk. We focus on the
minimum cost homomorphism problem for {\em reflexive} digraphs HHHH has a {\em Min-Max ordering}, i.e.,
if its vertices can be linearly ordered by <i<j, s<rir, js
\in A(H)is \in A(H)jr \in A(H)H$ which does not admit a Min-Max ordering, the minimum cost
homomorphism problem is NP-complete. Thus we obtain a full dichotomy
classification of the complexity of minimum cost homomorphism problems for
reflexive digraphs
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