Results 101 to 110 of about 119,953 (318)
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A new game chromatic number \(\chi^*_g(G)\) of a graph \(G\) is introduced. The authors first show that (i) if \(G\) is a connected bipartite graph with bipartition \((V_1,V_2)\), then \(\chi^*_g(G)= 2\) if and only if \(G\) has a vertex \(v\in V_1\) (say) such that \(N(v)= V_2\); and (ii) \(\chi^*_g(G)= \chi(G)\) (the chromatic number of \(G\)) if \(G\
Chen, G., Schelp, R.H., Shreve, W.E.
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This study demonstrates an aluminum‐based hybrid photoresist synthesized via molecular layer deposition (MLD) using trimethylaluminum and hydroquinone. The resist achieves sub‐20 nm resolution and virtually infinite silicon etch selectivity, enabling 40 nm‐wide, micrometer‐tall nanostructures.
Won‐Il Lee +8 more
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The incidence chromatic number of some graph
The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey (1993). They conjectured that every graph G can be incidence colored with Δ(G)+2 colors.
Liu Xikui, Li Yan
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Graphs obtained from collections of blocks
Given a collection of $d$-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially ...
Colton Magnant +2 more
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Could Edible Photonic Structures Be an Alternative to Traditional Food Coloring?
What if color in food came from photonic structures? This perspective introduces structural color as a potential next‐generation solution to replace conventional colorants in foods. It discusses edible photonic materials, their unique benefits, and the technological, safety, and consumer acceptance challenges that must be addressed to bring this ...
Miguel A. Cerqueira +5 more
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The Asymptotic value of the Locating-Chromatic number of $n$-ary Tree [PDF]
Yusuf Hafidh +2 more
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An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. We study anagram-free graph colouring and give bounds on the chromatic number. Alon et al.
Wilson, Tim E., Wood, David R.
core
On the degree of trees with game chromatic number 4 [PDF]
Ana Furtado +3 more
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