Zobrazeno 1 - 10
of 9 342
pro vyhledávání: '"A, Cranston"'
Autor:
Cranston, Daniel W.
Fix a planar graph $G$ and a list-assignment $L$ with $|L(v)|=10$ for all $v\in V(G)$. Let $\alpha$ and $\beta$ be $L$-colorings of $G$. A recoloring sequence from $\alpha$ to $\beta$ is a sequence of $L$-colorings, beginning with $\alpha$ and ending
Externí odkaz:
http://arxiv.org/abs/2411.00679
The problem \textsc{Token Jumping} asks whether, given a graph $G$ and two independent sets of \emph{tokens} $I$ and $J$ of $G$, we can transform $I$ into $J$ by changing the position of a single token in each step and having an independent set of to
Externí odkaz:
http://arxiv.org/abs/2408.04743
We study the problem of finding homomorphisms into odd cycles from planar graphs with high odd-girth. The Jaeger-Zhang conjecture states that every planar graph of odd-girth at least $4k+1$ admits a homomorphism to the odd cycle $C_{2k+1}$. The $k=1$
Externí odkaz:
http://arxiv.org/abs/2402.02689
Autor:
Cranston, Daniel W.
Let $G$ be a planar graph and $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a "token" on each vertex of $I_s$ and seek to move all tokens to $I_t$, by repeated "token jumping", removing a single token from one vertex
Externí odkaz:
http://arxiv.org/abs/2401.09543
For a graph $G$ and a list assignment $L$ with $|L(v)|=k$ for all $v$, an $L$-packing consists of $L$-colorings $\varphi_1,\cdots,\varphi_k$ such that $\varphi_i(v)\ne\varphi_j(v)$ for all $v$ and all distinct $i,j\in\{1,\ldots,k\}$. Let $\chi^{\star
Externí odkaz:
http://arxiv.org/abs/2401.01332
Autor:
Cranston, Daniel, Mahmoud, Reem
Publikováno v:
Discrete Math. Vol. 348(2), Feb. 2025, 114286
For every $r\ge13$, we show every 1-planar graph $G$ with $\Delta(G)\le r$ has an equitable $r$-coloring.
Comment: 9 figures
Comment: 9 figures
Externí odkaz:
http://arxiv.org/abs/2311.14915
Publikováno v:
BMC Psychiatry, Vol 24, Iss 1, Pp 1-13 (2024)
Abstract Background Tackling poor mental health in university students has been identified as a priority in higher education. However, there are few evidence-based prevention initiatives designed for students. Repetitive Negative Thought (RNT, e.g. w
Externí odkaz:
https://doaj.org/article/237d7f881c90486db566a70e436e634e
Autor:
Cranston, Daniel W.
Publikováno v:
European Journal of Combinatorics. Vol. 120. August 2024. Article 103960
Wegner conjectured that if $G$ is a planar graph with maximum degree $\Delta\ge 8$, then $\chi(G^2)\le \left\lfloor \frac32\Delta\right\rfloor +1$. This problem has received much attention, but remains open for all $\Delta\ge 8$. Here we prove an ana
Externí odkaz:
http://arxiv.org/abs/2308.09585
Autor:
Cranston, Daniel W., Yu, Gexin
Publikováno v:
Journal of Graph Theory. Vol. 107(3). July 2024. pp. 559-577
Hocquard, Kim, and Pierron constructed, for every even integer $D\ge 2$, a 2-degenerate graph $G_D$ with maximum degree $D$ such that $\omega(G_D^2)=\frac52D$. We prove for (a) all 2-degenerate graphs $G$ and (b) all graphs $G$ with $\mbox{mad}(G)<4$
Externí odkaz:
http://arxiv.org/abs/2305.11763
Autor:
Cranston, Daniel W., Feghali, Carl
Publikováno v:
Discrete Applied Math. Vol. 357, 15 November 2024, pp. 94-98
Let $G$ be a graph and $k$ be a positive integer, and let $Kc(G, k)$ denote the number of Kempe equivalence classes for the $k$-colorings of $G$. In 2006, Mohar noted that $Kc(G, k) = 1$ if $G$ is bipartite. As a generalization, we show that $Kc(G, k
Externí odkaz:
http://arxiv.org/abs/2303.09365