Bounded-degree graphs have arbitrarily large queue-number

David R. Wood

doi:10.46298/dmtcs.434

Bounded-degree graphs have arbitrarily large queue-number

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.434 ◽

2008 ◽

Vol Vol. 10 no. 1 (Graph and Algorithms) ◽

Author(s):

David R. Wood

Keyword(s):

Absolute Constant ◽

Bounded Degree ◽

Large N ◽

Vertex Graph ◽

International Audience ◽

Bounded Degree Graphs

Graphs and Algorithms International audience It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all \Delta ≥ 3 and for all sufﬁciently large n, there is a simple \Delta-regular n-vertex graph with queue-number at least c√\Delta_n^{1/2-1/\Delta} for some absolute constant c.

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Optimal induced universal graphs for bounded-degree graphs

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004117000706 ◽

2017 ◽

Vol 166 (1) ◽

pp. 61-74 ◽

Cited By ~ 1

Author(s):

NOGA ALON ◽

RAJKO NENADOV

Keyword(s):

Maximum Degree ◽

Constant Factor ◽

Induced Subgraph ◽

Bounded Degree ◽

Vertex Graph ◽

Bounded Degree Graphs ◽

Universal Graphs

AbstractWe show that for any constant Δ ≥ 2, there exists a graph Γ withO(nΔ / 2) vertices which contains everyn-vertex graph with maximum degree Δ as an induced subgraph. For odd Δ this significantly improves the best-known earlier bound and is optimal up to a constant factor, as it is known that any such graph must have at least Ω(nΔ/2) vertices.

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Cycle transversals in bounded degree graphs

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.533 ◽

2011 ◽

Vol Vol. 13 no. 1 (Graph and Algorithms) ◽

Author(s):

Marina Groshaus ◽

Pavol Hell ◽

Sulamita Klein ◽

Loana Tito Nogueira ◽

Fábio Protti

Keyword(s):

Approximation Algorithms ◽

Polynomial Time ◽

Maximum Degree ◽

Decomposition Theorem ◽

Np Hard ◽

Input Graph ◽

Bounded Degree ◽

Time Approximation ◽

International Audience ◽

Bounded Degree Graphs

Graphs and Algorithms International audience In this work we investigate the algorithmic complexity of computing a minimum C(k)-transversal, i.e., a subset of vertices that intersects all the chordless cycles with k vertices of the input graph, for a fixed k \textgreater= 3. For graphs of maximum degree at most three, we prove that this problem is polynomial-time solvable when k \textless= 4, and NP-hard otherwise. For graphs of maximum degree at most four, we prove that this problem is NP-hard for any fixed k \textgreater= 3. We also discuss polynomial-time approximation algorithms for computing C(3)-transversals in graphs of maximum degree at most four, based on a new decomposition theorem for such graphs that leads to useful reduction rules.

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A short note on conflict‐free coloring on closed neighborhoods of bounded degree graphs

Journal of Graph Theory ◽

10.1002/jgt.22670 ◽

2021 ◽

Author(s):

Sriram Bhyravarapu ◽

Subrahmanyam Kalyanasundaram ◽

Rogers Mathew

Keyword(s):

Short Note ◽

Bounded Degree ◽

Bounded Degree Graphs

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A remark on a theorem of A. E. Ingham.

10.46298/hrj.2006.155 ◽

2006 ◽

Vol Volume 29 ◽

Author(s):

K G Bhat ◽

K Ramachandra

Keyword(s):

Functional Equation ◽

Absolute Constant ◽

International Audience

International audience Referring to a theorem of A. E. Ingham, that for all $N\geq N_0$ (an absolute constant), the inequality $N^3\leq p\leq(N+1)^3$ is solvable in a prime $p$, we point out in this paper that it is implicit that he has actually proved that $\pi(x+h)-\pi(x) \sim h(\log x)^{-1}$ where $h=x^c$ and $c (>\frac{5}{8})$ is any constant. Further, we point out that even this stronger form can be proved without using the functional equation of $\zeta(s)$.

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