Compatible Eulerian circuits in Eulerian (di)graphs with generalized transition systems

Guo, Zhiwei; Li, Xueliang; Xu, Chuandong; Zhang, Shenggui

doi:10.1016/j.disc.2018.04.014

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…Compatibility systems: Theorems 2-4 actually hold in the setting of 'compatibility systems' which generalise edge colorings. Compatible cycles were considered for instance in [24,14].…”

Section: Discussionmentioning

confidence: 99%

Properly Colored Hamilton Cycles in Dirac-Type Hypergraphs

Antoniuk

Kamčev

Ruciński

2023

Electron. J. Combin.

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We consider a robust variant of Dirac-type problems in $k$-uniform hypergraphs. For instance, we prove that if $\mathcal{H}$ is a $k$-uniform hypergraph with minimum codegree at least $\left(\frac 12 + \gamma \right)n$, $\gamma >0$, and $n$ is sufficiently large, then any edge coloring $\phi$ satisfying appropriate local constraints yields a properly colored tight Hamilton cycle in $\mathcal{H}$. Similar results for loose cycles are also shown.

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“…Compatibility systems: Theorems 2-4 actually hold in the setting of 'compatibility systems' which generalise edge colorings. Compatible cycles were considered for instance in [24,14].…”

Section: Discussionmentioning

confidence: 99%

Properly Colored Hamilton Cycles in Dirac-Type Hypergraphs

Antoniuk

Kamčev

Ruciński

2023

Electron. J. Combin.

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“…Although we did not consider any counterparts of our results for digraphs, we realize that counterparts for digraphs analogous to Theorem 4.2.2 have been discussed (see [51,68,76]). Motivated by the ideas we explored in this chapter, it is natural to consider the existence of compatible spanning circuits visiting each vertex at least a specified number of times in arc-colored digraphs.…”

Section: Conclusion and An Open Problemmentioning

confidence: 99%

Compatible spanning circuits in edge-colored graphs

Guo

et al. 2020

Discrete Mathematics

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“…Compatibility systems: Theorems 2-4 actually hold in the setting of 'compatibility systems' which generalise edge colorings. Compatible cycles were considered for instance in [23,13].…”

Section: Connecting and Reservoir Lemmasmentioning

confidence: 99%