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3 070 (0,252s) •

Result

Cubic Cayley Graphs of Girth at most 6 and Their Hamiltonicity

Thomassen's conjecture states that a cubic graph with sufficiently large cyclic connectivity is hamiltonian. Even the following strong conjecture could hold: A cyclically 7-connected cubic graph is hamiltonian...

Pure mathematics

  • 2019
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  • Jimp
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  • Link
Result

Decomposing planar cubic graphs

The 3‐Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2‐regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cub...

Pure mathematics

  • 2018
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  • Jimp
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  • Link
Result

Counterexamples to Thomassen's Conjecture on Decomposition of Cubic Graphs

We construct an infinite family of counterexamples to Thomassen's conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree ...

Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

  • 2021
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  • Jimp
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  • Link
Result

Perfect matchings with restricted intersection in cubic graphs

A conjecture of G. Fan and A. Raspaud asserts that every bridgeless cubic graph contains three perfect matchings with empty intersection. We propose a possible in an embeddedgraph. We use this method to prove that bridgeless cub...

BA - Obecná matematika

  • 2010
    • •
  • Jx
Result

Hamiltonian decompositions of prisms over cubic graphs

A conjecture of Alspach and Rosenfeld states that the prism G Box K2 over any 3-connected cubic graph G has a decomposition into two Hamilton cycles. Using a method based on colored diagrams, we show this conjecture to hold...

BA - Obecná matematika

  • 2004
    • •
  • Jx
Result

A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs

The well-known dominating circuit conjecture has several interesting reformulations, for example conjectures of Fleischner, Matthews and Sumner, and Thomassen. We present another equivalent version of the dominating circuit conj...

BA - Obecná matematika

  • 2008
    • •
  • Jx
Result

Planar Emulators Conjecture Is Nearly True for Cubic Graphs

We prove that a cubic nonprojective graph cannot have a finite planar emulator, unless it belongs to one of two very special cases (in which the answer is open). This shows that Fellows' planar emulator conjecture, disproved for gen...

BA - Obecná matematika

  • 2015
    • •
  • Jx
    • •
  • Link
Result

Planar Emulators Conjecture Is Nearly True for Cubic Graphs

We prove that a cubic nonprojective graph cannot have a finite planar emulator, unless one of two very special cases happen (in which the answer is open). This shows that Fellows' planar emulator conjecture, disproved for general gr...

BA - Obecná matematika

  • 2013
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  • D
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  • Link
Result

Contractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks

We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonian), by Thomassen (every 4-connected line graph is Hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has ...

BA - Obecná matematika

  • 2008
    • •
  • Jx
Result

Exponentially many perfect matchings in cubic graphs

We prove a conjecture of Lovasz and Plummer that every cubic bridgeless graph contains an exponential number of perfect matchings.

BA - Obecná matematika

  • 2011
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  • Jx
    • •
  • Link
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