منابع مشابه
Eulerian digraphs and Dyck words, a bijection
The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph. 1. Background, and ...
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Soares [J. Graph Theory 1992] showed that the well known upper bound 3 δ+1n+ O(1) on the diameter of undirected graphs of order n and minimum degree δ also holds for digraphs, provided they are eulerian. In this paper we investigate if similar bounds can be given for digraphs that are, in some sense, close to being eulerian. In particular we show that a directed graph of order n and minimum deg...
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1 Cern2 y’s conjecture and the road coloring problem are two open problems concerning synchronization of !nite automata. We prove these conjectures in the special case that the vertices have uniform inand outdegrees. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملEmbedding quartic Eulerian digraphs on the plane
Minimal obstructions for embedding 4-regular Eulerian digraphs on the plane are considered in relation to the partial order defined by the cycle removal operation. Their basic properties are provided and all obstructions with parallel arcs are classified. ∗ The author is thankful for support from the Marsden Fund (Grant Number UOA-825) administered by the Royal Society of New Zealand. This gran...
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Let G be an eulerian digraph with a fixed edge coloring (not necessarily a proper edge coloring). A compatible circuit of G is an eulerian circuit such that every two consecutive edges in the circuit have different colors. We characterize the existence of compatible circuits for directed graphs avoiding certain vertices of outdegree three. Our result is analogous to a result of Kotzig for compa...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1971
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1971.101043