Planar graphs have bounded queue-number
We show that planar graphs have bounded queue-number, thus proving a conjecture of
Heath et al.[66] from 1992. The key to the proof is a new structural tool called layered …
Heath et al.[66] from 1992. The key to the proof is a new structural tool called layered …
Stack-number is not bounded by queue-number
Stack-number is not bounded by queue-number Page 1 COMBINATORICA Bolyai Society –
Springer-Verlag 0209–9683/122/$6.00 c 2022 János Bolyai Mathematical Society and …
Springer-Verlag 0209–9683/122/$6.00 c 2022 János Bolyai Mathematical Society and …
Queue layouts of planar 3-trees
A queue layout of a graph G consists of a linear order of the vertices of G and a partition of
the edges of G into queues, so that no two independent edges of the same queue are …
the edges of G into queues, so that no two independent edges of the same queue are …
An improved upper bound on the queue number of planar graphs
A k-queue layout is a special type of a linear layout, in which the linear order avoids (k+ 1)-
rainbows, that is, k+ 1 independent edges that pairwise form a nested pair. The optimization …
rainbows, that is, k+ 1 independent edges that pairwise form a nested pair. The optimization …
On the queue number of planar graphs
A k-queue layout is a special type of a linear layout, in which the linear order avoids (k+
1)(k+ 1)-rainbows, ie, k+ 1 k+ 1 independent edges that pairwise form a nested pair. The …
1)(k+ 1)-rainbows, ie, k+ 1 k+ 1 independent edges that pairwise form a nested pair. The …
The mixed page number of graphs
A linear layout of a graph typically consists of a total vertex order, and a partition of the
edges into sets either of non-crossing edges, called stacks, or of non-nested edges, called …
edges into sets either of non-crossing edges, called stacks, or of non-nested edges, called …
Parameterized algorithms for queue layouts
An h-queue layout of a graph G consists of a linear order of its vertices and a partition of its
edges into h queues, such that no two independent edges of the same queue nest. The …
edges into h queues, such that no two independent edges of the same queue nest. The …
Linear Layouts of Bipartite Planar Graphs
A linear layout of a graph G consists of a linear order,≺, of the vertices and a partition of the
edges. A part is called a queue (stack) if no two edges nest (cross), that is, two edges (v, w) …
edges. A part is called a queue (stack) if no two edges nest (cross), that is, two edges (v, w) …
Parameterized algorithms for queue layouts
An $ h $-queue layout of a graph $ G $ consists of a linear order of its vertices and a partition
of its edges into $ h $ sets, called queues, such that no two independent edges of the same …
of its edges into $ h $ sets, called queues, such that no two independent edges of the same …
Forbidden Patterns in Mixed Linear Layouts
D Haun, L Merker, S Pupyrev - arxiv preprint arxiv:2412.12786, 2024 - arxiv.org
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered
graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non …
graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non …