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)

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

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

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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)

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Subcubic edge-chromatic critical graphs have many edges

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

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The fractional chromatic number of the plane

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

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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)

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Planar Graphs have Independence Ratio at least 3/13

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

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

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

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A Note on Coloring Vertex-Transitive Graphs

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

[pdf] [doi]

Brooks’ Theorem and beyond

Journal of Graph Theory 80.3 (2015), pp. 199–225 (with D.W. Cranston)

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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)

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Graphs with χ=∆ Have Big Cliques

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

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A different short proof of Brooks’ theorem

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

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Coloring graphs with dense neighborhoods

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

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Coloring claw-free graphs with ∆-1 colors

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

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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.

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Partitioning and coloring graphs with degree constraints

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

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Graphs with chromatic number close to maximum degree

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

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∆-Critical graphs with small high vertex cliques

Journal of Combinatorial Theory, Series B 102.1 (2012), pp. 126–130.

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A strengthening of Brooks’ Theorem for line graphs

The Electronic Journal of Combinatorics 18.1 (2011), P145

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On hitting all maximum cliques with an independent set

Journal of Graph Theory 66.1 (2011), pp. 32–37

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A Novel Proof of the Heine-Borel Theorem

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

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A note on Reed’s conjecture

SIAM Journal on Discrete Mathematics 22.2 (2008), pp. 820–827

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Applying Gröbner basis techniques to group theory

Journal of Pure and Applied Algebra 210.1 (2007), pp. 137–140

[pdf] [doi]

The Borodin-Kostochka conjecture for graphs containing a doubly critical edge

The Electronic Journal of Combinatorics 14 (2007), N22.

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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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Some bounds on convex combinations of ω and χ for decompositions into many parts

arXiv:math/0512291 (2005)

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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."

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