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pro vyhledávání: '"primary 05c15"'
In this paper, we explore algebraic approaches to $d$-improper and $t$-clustered colourings, where the colouring constraints are relaxed to allow some monochromatic edges. Bilu [J. Comb. Theory Ser. B, 96(4):608-613, 2006] proved a generalization of
Externí odkaz:
http://arxiv.org/abs/2411.06941
Autor:
Antoniuk, Sylwia, Reiher, Christian
For a bounded measurable set $A\subseteq \mathbb{R}$ we denote the Lebesgue measure of $\{(x, y)\in A^2\colon x\le y\le x+1\}$ by $\Phi(A)$. We prove that if $I=A_1\cup\dots\cup A_{k+1}$ partitions an interval $I$ of length $L$ into $k+1$ measurable
Externí odkaz:
http://arxiv.org/abs/2410.23868
Autor:
Tom, Foster, Vailaya, Aarush
We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are $e$-positive for cycles. Then we prove that attaching a cycle to a graph preserves the $e$-positivity of these pieces.
Externí odkaz:
http://arxiv.org/abs/2410.21762
Given a graph $G$ and two graph homomorphisms $\alpha$ and $\beta$ from $G$ to a fixed graph $H$, the problem $H$-Recoloring asks whether there is a transformation from $\alpha$ to $\beta$ that changes the image of a single vertex at each step and ke
Externí odkaz:
http://arxiv.org/abs/2410.12687
Autor:
Minyard, Mitchell, Sepanski, Mark R.
A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen
Externí odkaz:
http://arxiv.org/abs/2410.05422
A vertex coloring of a graph is said to be pseudocomplete if, for any two distinct colors, there exists at least one edge with those two colors as its end vertices. The pseudoachromatic number of a graph is the greatest number of colors possible used
Externí odkaz:
http://arxiv.org/abs/2408.16739
Autor:
Korchmaros, Annachiara
The undirected underlying graph of a 2-quasi best match graph (2-qBMG) is proven not to contain any induced graph isomorphic to $P_6$ or $C_6$. This new feature allows for the investigation of 2-BMGs further by exploiting the numerous known results o
Externí odkaz:
http://arxiv.org/abs/2408.09997
Autor:
Ciardo, Lorenzo
Information-processing tasks modelled by homomorphisms between relational structures can witness quantum advantage when entanglement is used as a computational resource. We prove that the occurrence of quantum advantage is determined by the same type
Externí odkaz:
http://arxiv.org/abs/2404.13186
For a graph $G$, the $k$-colouring graph of $G$ has vertices corresponding to proper $k$-colourings of $G$ and edges between colourings that differ at a single vertex. The graph supports the Glauber dynamics Markov chain for $k$-colourings, and has b
Externí odkaz:
http://arxiv.org/abs/2402.04237
Autor:
Thornton, Riley
We show that, for every $\epsilon>0$, the 4-regular tree has an fiid 4-coloring where a given vertex is assigned the 4th color with probability at most $\epsilon$. We also construct 5-colorings of $T_6$ improving known bounds on the measurable and ap
Externí odkaz:
http://arxiv.org/abs/2402.02575