Queue number¶
The minimum number of edge queues needed in a vertex ordering of a graph so no two edges in the same queue are properly nested.
Core Idea¶
Queue number is the FIFO analogue of book thickness and relates linear layouts to track layouts, layered drawings, planar graphs, subdivisions, and bounded structural parameters. A total vertex order is chosen, edges are partitioned into queues, and each queue is checked for absence of a pair with endpoints ordered a<c<d<b; optimization minimizes the queue count over orders and partitions. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Queue number belongs to graph layouts and structural graph theory and is useful where the analyst can specify the typed graph layouts and structural graph theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the graph class, total vertex ordering, edge endpoint convention, proper-nesting predicate, queue partition, treatment of shared endpoints, minimum objective, and construction or lower-bound proof are explicit. The scope is broad within that domain but bounded by the need for the graph class, total vertex ordering, edge endpoint convention, proper-nesting predicate, queue partition, treatment of shared endpoints, minimum objective, and construction or lower-bound proof are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the graph class, total vertex ordering, edge endpoint convention, proper-nesting predicate, queue partition, treatment of shared endpoints, minimum objective, and construction or lower-bound proof are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Queue number can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Queue number. Queue number compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed graph layouts and structural graph theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the graph class, total vertex ordering, edge endpoint convention, proper-nesting predicate, queue partition, treatment of shared endpoints, minimum objective, and construction or lower-bound proof are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of graph layouts and structural graph theory because they reuse the typed graph layouts and structural graph theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, A total vertex order is chosen, edges are partitioned into queues, and each queue is checked for absence of a pair with endpoints ordered a<c<d<b; optimization minimizes the queue count over orders and partitions., and type the carrier, state every parameter and convention in the definition, test that the graph class, total vertex ordering, edge endpoint convention, proper-nesting predicate, queue partition, treatment of shared endpoints, minimum objective, and construction or lower-bound proof are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Queue number Domain-specific
Parents (1) — more general patterns this builds on
-
Queue number is a kind of Partition Prime
The proposed strict upward parent is
prime:partition.
Hierarchy path (1) — routes to 1 parentless root
- Queue number → Partition → Set and Membership
Neighborhood in Abstraction Space¶
Queue number sits in a crowded region of the domain-specific corpus (3rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Graph Coloring & Labeling (14 abstractions)
Nearest neighbors
- Split graph — 0.94
- Graph bandwidth — 0.94
- Treewidth — 0.94
- Join (graph theory) — 0.94
- Strong product of graphs — 0.93
Computed from structural-signature embeddings · 2026-09-08