Results 21 to 30 of about 9,631,849 (193)
Dominator Chromatic numbers of orientations of trees [PDF]
Open Journal of Discrete Applied Mathematics, 2021 In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences as well as bounds on other orientations of oft studied tree topologies including generalized stars ...
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Proper orientations and proper chromatic number
Journal of Combinatorial Theory, Series B, 2023 The proper chromatic number $\Vecχ(G)$ of a graph $G$ is the minimum $k$ such that there exists an orientation of the edges of $G$ with all vertex-outdegrees at most $k$ and such that for any adjacent vertices, the outdegrees are different. Two major conjectures about the proper chromatic number are resolved.
Yaobin Chen, Bojan Mohar, Hehui Wu
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The Choice Number Versus the Chromatic Number for Graphs Embeddable on Orientable Surfaces [PDF]
The Electronic Journal of Combinatorics, 2021 We show that for loopless $6$-regular triangulations on the torus the gap between the choice number and chromatic number is at most $2$. We also show that the largest gap for graphs embeddable in an orientable surface of genus $g$ is of the order $\Theta(\sqrt{g})$, and moreover for graphs with chromatic number of the order $o(\sqrt{g}/\log_{2}(g ...
Brahadeesh Sankarnarayanan +1 more
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The fractional chromatic number of triangle-free subcubic graphs [PDF]
, 2014 Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14 / 5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free ...
Král’, Daniel +5 more
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The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards, Keith
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Balanced Signings and the Chromatic Number of Oriented Matroids [PDF]
Combinatorics, Probability and Computing, 2006 We consider the problem of reorienting an oriented matroid so that all its cocircuits are ‘as balanced as possible in ratio’. It is well known that any oriented matroid having no coloops has a totally cyclic reorientation, a reorientation in which every signed cocircuit $B = \{B^+, B^-\}$ satisfies $B^+, B^- \neq \emptyset$.
Luis A. Goddyn +2 more
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Degrees in Oriented Hypergraphs and Ramsey p-Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2012 The family $D(k,m)$ of graphs having an orientation such that for every vertex $v \in V(G)$ either (outdegree) $\deg^+(v) \le k$ or (indegree) $\deg^-(v) \le m$ have been investigated recently in several papers because of the role $D(k,m)$ plays in the efforts to estimate the maximum directed cut in digraphs and the minimum cover of digraphs by ...
Caro, Y., Hansberg Pastor, Adriana
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Orientations of graphs with uncountable chromatic number [PDF]
Journal of Graph Theory, 2017 AbstractMotivated by an old conjecture of P. Erdős and V. Neumann‐Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountablechromatic numberif its vertices cannot be covered by countably many independent sets, and a digraph has ...
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A Compound Computational Model for Filling-In Processes Triggered by Edges: Watercolor Illusions
Frontiers in Neuroscience, 2019 The goal of our research was to develop a compound computational model with the ability to predict different variations of the “watercolor effects” and additional filling-in effects that are triggered by edges.
Hadar Cohen-Duwek, Hedva Spitzer
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Proving a conjecture on chromatic polynomials by counting the number of acyclic orientations [PDF]
Journal of Graph Theory, 2020 AbstractThe chromatic polynomial of a graph of order can be expressed as , where is interpreted as the number of broken‐cycle‐free spanning subgraphs of with exactly components. The parameter is the mean size of a broken‐cycle‐free spanning subgraph of .
Fengming Dong +5 more
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