Bar -visibility graphs.
Dean, Alice M., Evans, William, Gethner, Ellen, Laison, Joshua D., Safari, Mohammad Ali, Trotter, William T. (2007)
Journal of Graph Algorithms and Applications
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Dean, Alice M., Evans, William, Gethner, Ellen, Laison, Joshua D., Safari, Mohammad Ali, Trotter, William T. (2007)
Journal of Graph Algorithms and Applications
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Juvan, Martin, Mohar, Bojan, Thomas, Robin (1999)
The Electronic Journal of Combinatorics [electronic only]
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Yuehua Bu, Ko-Wei Lih, Weifan Wang (2011)
Discussiones Mathematicae Graph Theory
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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu,...
Dujmović, Vida, Pór, Attila, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Oleg V. Borodin, Anna O. Ivanova (2013)
Discussiones Mathematicae Graph Theory
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We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40 [...] +1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Xin Zhang, Guizhen Liu (2013)
Open Mathematics
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If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity...
Xin Zhang, Yong Yu, Guizhen Liu (2011)
Open Mathematics
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A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.
Dillencourt, Michael B., Eppstein, David, Hirschberg, Daniel S. (2000)
Journal of Graph Algorithms and Applications
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Di Giacomo, Emilio, Didimo, Walter, Liotta, Giuseppe, Palladino, Pietro (2010)
Journal of Graph Algorithms and Applications
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Luczak, Tomasz (1994)
The Electronic Journal of Combinatorics [electronic only]
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Oleg V. Borodin (1990)
Mathematica Slovaca
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