Landon Rabern Bibliography

Coloring (P_{5}, gem)-free graphs with ∆ − 1 colors

arXiv:2006.02015 (2020) (with D.W. Cranston, H. Lafayette)

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Improved lower bounds on the number of edges in list critical and online list critical graphs

Journal of Combinatorial Theory, Series B 140 (2020), pp. 147–170 (with H.A. Kierstead).

[pdf] [doi]

The Hilton-Zhao Conjecture is True for Graphs with Maximum Degree 4

SIAM Journal on Discrete Mathematics 33.3 (2019), pp. 1228–1241 (with D.W. Cranston).

[pdf] [doi]

Edge lower bounds for list critical graphs, via discharging

Combinatorica 38.5 (2018), pp. 1045– 1065 (with D.W. Cranston).

[pdf] [doi]

A better lower bound on average degree of k-list-critical graphs

The Electronic Journal of Combinatorics 25.1 (2018), P1.51.

[pdf] [doi]

Beyond Degree Choosability

The Electronic Journal of Combinatorics 24.3 (2017), P3.29 (with D.W. Cranston)

[pdf] [doi]

List-Coloring Claw-Free Graphs with ∆-1 Colors

SIAM Journal on Discrete Mathematics 31.2 (2017), pp. 726–748 (with D.W. Cranston)

[pdf] [doi]

Short fans and the 5/6 bound for line graphs

SIAM Journal on Discrete Mathematics 31.3 (2017), pp. 2039–2063 (with D.W. Cranston)

[pdf] [doi]

Subcubic edge-chromatic critical graphs have many edges

Journal of Graph Theory 86.1 (2017), pp. 122–136 (with D.W. Cranston)

[pdf] [doi]

The fractional chromatic number of the plane

Combinatorica 37.5 (2017), pp. 837–861 (with D.W. Cranston)

[pdf] [doi]

Extracting list colorings from large independent sets

Journal of Graph Theory 86.3 (2017), pp. 315–328 (with H.A. Kierstead)

[pdf] [doi]

Painting Squares in ∆^{2} − 1 Shades

The Electronic Journal of Combinatorics 23.2 (2016), P2.50 (with D.W. Cranston)

[pdf] [doi]

Planar Graphs have Independence Ratio at least 3/13

The Electronic Journal of Combinatorics 23.3 (2016), P3.45 (with D.W. Cranston)

[pdf] [doi]

A Better Lower Bound on Average Degree of 4-List- Critical Graphs

The Electronic Journal of Combinatorics 23.3 (2016), P3.37.

[pdf] [doi]

A Note on Coloring Vertex-Transitive Graphs

The Electronic Journal of Combinatorics 22.2 (2015), P2.1 (with D.W. Cranston)

[pdf] [doi]

Coloring a graph with ∆-1 colors: Conjectures equivalent to the Borodin–Kostochka conjecture that appear weaker

European Journal of Combinatorics 44 (2015), pp. 23–42 (with D.W. Cranston)

[pdf] [doi]

Graphs with χ=∆ Have Big Cliques

SIAM Journal on Discrete Mathematics 29.4 (2015), pp. 1792– 1814 (with D.W. Cranston)

[pdf] [doi]

A different short proof of Brooks’ theorem

Discussiones Mathematicae Graph Theory 34.3 (2014), pp. 633–634

[pdf] [doi]

Coloring graphs with dense neighborhoods

Journal of Graph Theory 76.4 (2014), pp. 323–340

[pdf] [doi]

Coloring claw-free graphs with ∆-1 colors

SIAM Journal on Discrete Mathematics 27.1 (2013), pp. 534–549 (with D.W. Cranston)

[pdf] [doi]

Coloring Graphs from Almost Maximum Degree Sized Palettes

PhD thesis. Arizona State University, 2013 (Supervisor: H.A. Kierstead)

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Destroying noncomplete regular components in graph partitions

Journal of Graph Theory 72.2 (2013), pp. 123–127.

[pdf] [doi]

Partitioning and coloring graphs with degree constraints

Discrete Mathematics 313.9 (2013), pp. 1028–1034.

[pdf] [doi]

Graphs with chromatic number close to maximum degree

Discrete Mathematics 312.6 (2012), pp. 1273–1281 (with A.V. Kostochka and M. Stiebitz).

[pdf] [doi]

A strengthening of Brooks’ Theorem for line graphs

The Electronic Journal of Combinatorics 18.1 (2011), P145

[pdf] [doi]

A Novel Proof of the Heine-Borel Theorem

arXiv:0808.0844 (2008) (with B. Rabern and M. Macauley).

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A knowledge-based system for graph theory, demonstrated by partial proofs for graph-colouring problems

MATCH Communications in Mathematical and in Computer Chemistry 58 (2007), pp. 445--460 (with D. Gernet)

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Properties of Magic Squares of Squares

Rose-Hulman Undergraduate Mathematics Journal 4.1 (2003)

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"We do not need more tools, we need hands to pick up the tools"

"Formalism. formalism! give us our formalism, for our minds are weak and our vision poor."

public Delegate Turtle Turtle(Turtle turtle);

public Delegate Turtle Turtle(Turtle turtle);