Supereulerian 2-edge-coloured graphs
J{\o}rgen Bang-Jensen, Thomas Bellitto, Anders Yeo

TL;DR
This paper introduces polynomial algorithms for identifying supereulerian properties in 2-edge-coloured graphs, explores the structure of M-closed graphs, and establishes NP-completeness results for general cases.
Contribution
It provides a polynomial-time method to find eulerian factors in 2-edge-coloured graphs and characterizes supereulerian graphs within M-closed classes, advancing understanding of their structure.
Findings
Polynomial algorithm for eulerian factor detection
Characterization of supereulerian graphs in M-closed classes
NP-completeness of deciding supereulerian property in general graphs
Abstract
A 2-edge-coloured graph is {\bf supereulerian} if contains a spanning closed trail in which the edges alternate in colours. An {\bf eulerian factor} of a 2-edge-coloured graph is a collection of vertex disjoint induced subgraphs which cover all the vertices of such that each of these subgraphs is supereulerian. We give a polynomial algorithm to test if a 2-edge-coloured graph has an eulerian factor and to produce one when it exists. A 2-edge-coloured graph is {\bf (trail-)colour-connected} if it contains a pair of alternating -paths (-trails) whose union is an alternating closed walk for every pair of distinct vertices . A 2-edge-coloured graph is {\bf M-closed} if is an edge of whenever some vertex is joined to both and by edges of the same colour. M-closed 2-edge-coloured graphs, introduced in \cite{balbuenaDMTCS21}, form a rich…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems
